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A design conundrum : minimal client code vs polymorphic design

I am handling several categories of food, catagorized as
non-cooked meat
cooked meat
other food not of the two previous categories
where meat can be pork or beef meat.
Functionally I can characterize in which of the three previous food categories food is (including knowing if the meat is beef or pork if the food is not other) thank to a int ID. Then I can treat the food by outputting some characteristics of it at a given row of a some given array.
In terms of code, I would like to be able to write something like :
// client code
Food SomeFood = new Food(ID); // int ID is given
SomeFood.FillTo(thearray, therow); // where object[,] thearray has to be filled and int therow is the row to be filled
where FillTo depends on the type of food (cooked of not + type of meat included).
Of course I could design one an only "client" class Food wrapping all the info such that for SomeFood FillTo fills infos to thearray according to the type of SomeFood, but I don't want to do this.
I would like to define a class hierarchy as follows : a base Food class from which derive Meat and CookedMeat classes such that the non-(cooked or not)-meat case would be handled by the base class Food, the two others cases being handled by derived classes, the type of meat being handled by an enum member common to the two derived classes.
My problem is the following : I feel that wanting to write a minimal client code as the one above implies necessarily that I don't need a class hierarchy design, and that if I want a class hierarchy designed, then I am forced to write to decouple the determination of the type of food by an ID and that I have then, according to it, to instanciate the right type of food :
// more verbose client code
// int ID is given
ATypeOfFood = gettypefrom(ID);
if (TypeOfFood.Other == ATypeOfFood)
{
AFood = new OtherFood(ID);
OtherFood.FillTo(thearray, therow);
}
else if (TypeOfFood.CookedMeat == ATypeOfFood)
{
AFood = new CookedMeat(ID);
OtherFood.FillTo(thearray, therow);
}
// etc etc ...
Am I wrong ?
Is it possible to encompass somehow the Food AFood = new ADerivedClass(ID) inside the base class Food ? Or even outside through a setting function ? (I can see how to do this with pointers in c++, but not in c# as one cannot instantiate base class before setting it.)
Remark. The c# tag is there because I am into doing this in a c# language project, language I am new to and that I am learning.

This is a pretty broad question, but let's try.
First of all, this is of course about balancing. You don't want to sacrifice "users have a clean API to program against" for "my library is super-well defined regarding OOP".
Guiding mantras for "good APIs" - they
make it easy to do the right thing, and hard to do the wrong thing
should be prepared for future visions
Meaning: when implementing a solution, you remember about yagni - you avoid implementing something that you don't need today. But: when you provide an API to "clients", then you don't want to break them with future releases.
Thus: you have to step back and clarify for yourself what the intended use cases are - from the perspective of the users of your API. You make sure that your API allows them to write expressive, robust code to do what they have to do. And to a certain degree, you want to be prepared for future changes that you maybe can foresee today already.
Coming from there:
derive an object model that is helpful to the users of your API
when you got a clear picture of that, then look into the question how to implement that model in a nice, clean fashion

Why not inherit from List<T>?

When planning out my programs, I often start with a chain of thought like so:
A football team is just a list of football players. Therefore, I should represent it with:
var football_team = new List<FootballPlayer>();
The ordering of this list represent the order in which the players are listed in the roster.
But I realize later that teams also have other properties, besides the mere list of players, that must be recorded. For example, the running total of scores this season, the current budget, the uniform colors, a string representing the name of the team, etc..
So then I think:
Okay, a football team is just like a list of players, but additionally, it has a name (a string) and a running total of scores (an int). .NET does not provide a class for storing football teams, so I will make my own class. The most similar and relevant existing structure is List<FootballPlayer>, so I will inherit from it:
class FootballTeam : List<FootballPlayer>
{
public string TeamName;
public int RunningTotal
}
But it turns out that a guideline says you shouldn't inherit from List<T>. I'm thoroughly confused by this guideline in two respects.
Why not?
Apparently List is somehow optimized for performance. How so? What performance problems will I cause if I extend List? What exactly will break?
Another reason I've seen is that List is provided by Microsoft, and I have no control over it, so I cannot change it later, after exposing a "public API". But I struggle to understand this. What is a public API and why should I care? If my current project does not and is not likely to ever have this public API, can I safely ignore this guideline? If I do inherit from List and it turns out I need a public API, what difficulties will I have?
Why does it even matter? A list is a list. What could possibly change? What could I possibly want to change?
And lastly, if Microsoft did not want me to inherit from List, why didn't they make the class sealed?
What else am I supposed to use?
Apparently, for custom collections, Microsoft has provided a Collection class which should be extended instead of List. But this class is very bare, and does not have many useful things, such as AddRange, for instance. jvitor83's answer provides a performance rationale for that particular method, but how is a slow AddRange not better than no AddRange?
Inheriting from Collection is way more work than inheriting from List, and I see no benefit. Surely Microsoft wouldn't tell me to do extra work for no reason, so I can't help feeling like I am somehow misunderstanding something, and inheriting Collection is actually not the right solution for my problem.
I've seen suggestions such as implementing IList. Just no. This is dozens of lines of boilerplate code which gains me nothing.
Lastly, some suggest wrapping the List in something:
class FootballTeam
{
public List<FootballPlayer> Players;
}
There are two problems with this:
It makes my code needlessly verbose. I must now call my_team.Players.Count instead of just my_team.Count. Thankfully, with C# I can define indexers to make indexing transparent, and forward all the methods of the internal List... But that's a lot of code! What do I get for all that work?
It just plain doesn't make any sense. A football team doesn't "have" a list of players. It is the list of players. You don't say "John McFootballer has joined SomeTeam's players". You say "John has joined SomeTeam". You don't add a letter to "a string's characters", you add a letter to a string. You don't add a book to a library's books, you add a book to a library.
I realize that what happens "under the hood" can be said to be "adding X to Y's internal list", but this seems like a very counter-intuitive way of thinking about the world.
My question (summarized)
What is the correct C# way of representing a data structure, which, "logically" (that is to say, "to the human mind") is just a list of things with a few bells and whistles?
Is inheriting from List<T> always unacceptable? When is it acceptable? Why/why not? What must a programmer consider, when deciding whether to inherit from List<T> or not?

There are some good answers here. I would add to them the following points.
What is the correct C# way of representing a data structure, which, "logically" (that is to say, "to the human mind") is just a list of things with a few bells and whistles?
Ask any ten non-computer-programmer people who are familiar with the existence of football to fill in the blank:
A football team is a particular kind of _____
Did anyone say "list of football players with a few bells and whistles", or did they all say "sports team" or "club" or "organization"? Your notion that a football team is a particular kind of list of players is in your human mind and your human mind alone.
List<T> is a mechanism. Football team is a business object -- that is, an object that represents some concept that is in the business domain of the program. Don't mix those! A football team is a kind of team; it has a roster, a roster is a list of players. A roster is not a particular kind of list of players. A roster is a list of players. So make a property called Roster that is a List<Player>. And make it ReadOnlyList<Player> while you're at it, unless you believe that everyone who knows about a football team gets to delete players from the roster.
Is inheriting from List<T> always unacceptable?
Unacceptable to whom? Me? No.
When is it acceptable?
When you're building a mechanism that extends the List<T> mechanism.
What must a programmer consider, when deciding whether to inherit from List<T> or not?
Am I building a mechanism or a business object?
But that's a lot of code! What do I get for all that work?
You spent more time typing up your question that it would have taken you to write forwarding methods for the relevant members of List<T> fifty times over. You're clearly not afraid of verbosity, and we are talking about a very small amount of code here; this is a few minutes work.
UPDATE
I gave it some more thought and there is another reason to not model a football team as a list of players. In fact it might be a bad idea to model a football team as having a list of players too. The problem with a team as/having a list of players is that what you've got is a snapshot of the team at a moment in time. I don't know what your business case is for this class, but if I had a class that represented a football team I would want to ask it questions like "how many Seahawks players missed games due to injury between 2003 and 2013?" or "What Denver player who previously played for another team had the largest year-over-year increase in yards ran?" or "Did the Piggers go all the way this year?"
That is, a football team seems to me to be well modeled as a collection of historical facts such as when a player was recruited, injured, retired, etc. Obviously the current player roster is an important fact that should probably be front-and-center, but there may be other interesting things you want to do with this object that require a more historical perspective.

Wow, your post has an entire slew of questions and points. Most of the reasoning you get from Microsoft is exactly on point. Let's start with everything about List<T>
List<T> is highly optimized. Its main usage is to be used as a private member of an object.
Microsoft did not seal it because sometimes you might want to create a class that has a friendlier name: class MyList<T, TX> : List<CustomObject<T, Something<TX>> { ... }. Now it's as easy as doing var list = new MyList<int, string>();.
CA1002: Do not expose generic lists: Basically, even if you plan to use this app as the sole developer, it's worthwhile to develop with good coding practices, so they become instilled into you and second nature. You are still allowed to expose the list as an IList<T> if you need any consumer to have an indexed list. This lets you change the implementation within a class later on.
Microsoft made Collection<T> very generic because it is a generic concept... the name says it all; it is just a collection. There are more precise versions such as SortedCollection<T>, ObservableCollection<T>, ReadOnlyCollection<T>, etc. each of which implement IList<T> but not List<T>.
Collection<T> allows for members (i.e. Add, Remove, etc.) to be overridden because they are virtual. List<T> does not.
The last part of your question is spot on. A Football team is more than just a list of players, so it should be a class that contains that list of players. Think Composition vs Inheritance. A Football team has a list of players (a roster), it isn't a list of players.
If I were writing this code, the class would probably look something like so:
public class FootballTeam<T>//generic class
{
// Football team rosters are generally 53 total players.
private readonly List<T> _roster = new List<T>(53);
public IList<T> Roster
{
get { return _roster; }
}
// Yes. I used LINQ here. This is so I don't have to worry about
// _roster.Length vs _roster.Count vs anything else.
public int PlayerCount
{
get { return _roster.Count(); }
}
// Any additional members you want to expose/wrap.
}

class FootballTeam : List<FootballPlayer>
{
public string TeamName;
public int RunningTotal;
}
Previous code means: a bunch of guys from the street playing football, and they happen to have a name. Something like:
Anyway, this code (from m-y's answer)
public class FootballTeam
{
// A team's name
public string TeamName;
// Football team rosters are generally 53 total players.
private readonly List<T> _roster = new List<T>(53);
public IList<T> Roster
{
get { return _roster; }
}
public int PlayerCount
{
get { return _roster.Count(); }
}
// Any additional members you want to expose/wrap.
}
Means: this is a football team which has management, players, admins, etc. Something like:
This is how is your logic presented in pictures…

This is a classic example of composition vs inheritance.
In this specific case:
Is the team a list of players with added behavior
or
Is the team an object of its own that happens to contain a list of players.
By extending List you are limiting yourself in a number of ways:
You cannot restrict access (for example, stopping people changing the roster). You get all the List methods whether you need/want them all or not.
What happens if you want to have lists of other things as well. For example, teams have coaches, managers, fans, equipment, etc. Some of those might well be lists in their own right.
You limit your options for inheritance. For example you might want to create a generic Team object, and then have BaseballTeam, FootballTeam, etc. that inherit from that. To inherit from List you need to do the inheritance from Team, but that then means that all the various types of team are forced to have the same implementation of that roster.
Composition - including an object giving the behavior you want inside your object.
Inheritance - your object becomes an instance of the object that has the behavior you want.
Both have their uses, but this is a clear case where composition is preferable.

As everyone has pointed out, a team of players is not a list of players. This mistake is made by many people everywhere, perhaps at various levels of expertise. Often the problem is subtle and occasionally very gross, as in this case. Such designs are bad because these violate the Liskov Substitution Principle. The internet has many good articles explaining this concept e.g., http://en.wikipedia.org/wiki/Liskov_substitution_principle
In summary, there are two rules to be preserved in a Parent/Child relationship among classes:
a Child should require no characteristic less than what completely defines the Parent.
a Parent should require no characteristic in addition to what completely defines the Child.
In other words, a Parent is a necessary definition of a child, and a child is a sufficient definition of a Parent.
Here is a way to think through ones solution and apply the above principle that should help one avoid such a mistake. One should test ones hypothesis by verifying if all the operations of a parent class are valid for the derived class both structurally and semantically.
Is a football team a list of football players? ( Do all properties of a list apply to a team in the same meaning)
Is a team a collection of homogenous entities? Yes, team is a collection of Players
Is the order of inclusion of players descriptive of the state of the team and does the team ensure that the sequence is preserved unless explicitly changed? No, and No
Are players expected to be included/dropped based on their sequencial position in the team? No
As you see, only the first characteristic of a list is applicable to a team. Hence a team is not a list. A list would be a implementation detail of how you manage your team, so it should only be used to store the player objects and be manipulated with methods of Team class.
At this point I'd like to remark that a Team class should, in my opinion, not even be implemented using a List; it should be implemented using a Set data structure (HashSet, for example) in most cases.

What if the FootballTeam has a reserves team along with the main team?
class FootballTeam
{
List<FootballPlayer> Players { get; set; }
List<FootballPlayer> ReservePlayers { get; set; }
}
How would you model that with?
class FootballTeam : List<FootballPlayer>
{
public string TeamName;
public int RunningTotal
}
The relationship is clearly has a and not is a.
or RetiredPlayers?
class FootballTeam
{
List<FootballPlayer> Players { get; set; }
List<FootballPlayer> ReservePlayers { get; set; }
List<FootballPlayer> RetiredPlayers { get; set; }
}
As a rule of thumb, if you ever want to inherit from a collection, name the class SomethingCollection.
Does your SomethingCollection semantically make sense? Only do this if your type is a collection of Something.
In the case of FootballTeam it doesn't sound right. A Team is more than a Collection. A Team can have coaches, trainers, etc as the other answers have pointed out.
FootballCollection sounds like a collection of footballs or maybe a collection of football paraphernalia. TeamCollection, a collection of teams.
FootballPlayerCollection sounds like a collection of players which would be a valid name for a class that inherits from List<FootballPlayer> if you really wanted to do that.
Really List<FootballPlayer> is a perfectly good type to deal with. Maybe IList<FootballPlayer> if you are returning it from a method.
In summary
Ask yourself
Is X a Y? or Has X a Y?
Do my class names mean what they are?

Design > Implementation
What methods and properties you expose is a design decision. What base class you inherit from is an implementation detail. I feel it's worth taking a step back to the former.
An object is a collection of data and behaviour.
So your first questions should be:
What data does this object comprise in the model I'm creating?
What behaviour does this object exhibit in that model?
How might this change in future?
Bear in mind that inheritance implies an "isa" (is a) relationship, whereas composition implies a "has a" (hasa) relationship. Choose the right one for your situation in your view, bearing in mind where things might go as your application evolves.
Consider thinking in interfaces before you think in concrete types, as some people find it easier to put their brain in "design mode" that way.
This isn't something everyone does consciously at this level in day to day coding. But if you're mulling this sort of topic, you're treading in design waters. Being aware of it can be liberating.
Consider Design Specifics
Take a look at List<T> and IList<T> on MSDN or Visual Studio. See what methods and properties they expose. Do these methods all look like something someone would want to do to a FootballTeam in your view?
Does footballTeam.Reverse() make sense to you? Does footballTeam.ConvertAll<TOutput>() look like something you want?
This isn't a trick question; the answer might genuinely be "yes". If you implement/inherit List<Player> or IList<Player>, you're stuck with them; if that's ideal for your model, do it.
If you decide yes, that makes sense, and you want your object to be treatable as a collection/list of players (behaviour), and you therefore want to implement ICollection<Player> or IList<Player>, by all means do so. Notionally:
class FootballTeam : ... ICollection<Player>
{
...
}
If you want your object to contain a collection/list of players (data), and you therefore want the collection or list to be a property or member, by all means do so. Notionally:
class FootballTeam ...
{
public ICollection<Player> Players { get { ... } }
}
You might feel that you want people to be able to only enumerate the set of players, rather than count them, add to them or remove them. IEnumerable<Player> is a perfectly valid option to consider.
You might feel that none of these interfaces are useful in your model at all. This is less likely (IEnumerable<T> is useful in many situations) but it's still possible.
Anyone who attempts to tell you that one of these it is categorically and definitively wrong in every case is misguided. Anyone who attempts to tell you it is categorically and definitively right in every case is misguided.
Move on to Implementation
Once you've decided on data and behaviour, you can make a decision about implementation. This includes which concrete classes you depend on via inheritance or composition.
This may not be a big step, and people often conflate design and implementation since it's quite possible to run through it all in your head in a second or two and start typing away.
A Thought Experiment
An artificial example: as others have mentioned, a team is not always "just" a collection of players. Do you maintain a collection of match scores for the team? Is the team interchangeable with the club, in your model? If so, and if your team isa collection of players, perhaps it also isa collection of staff and/or a collection of scores. Then you end up with:
class FootballTeam : ... ICollection<Player>,
ICollection<StaffMember>,
ICollection<Score>
{
....
}
Design notwithstanding, at this point in C# you won't be able to implement all of these by inheriting from List<T> anyway, since C# "only" supports single inheritance. (If you've tried this malarkey in C++, you may consider this a Good Thing.) Implementing one collection via inheritance and one via composition is likely to feel dirty. And properties such as Count become confusing to users unless you implement ILIst<Player>.Count and IList<StaffMember>.Count etc. explicitly, and then they're just painful rather than confusing. You can see where this is going; gut feeling whilst thinking down this avenue may well tell you it feels wrong to head in this direction (and rightly or wrongly, your colleagues might also if you implemented it this way!)
The Short Answer (Too Late)
The guideline about not inheriting from collection classes isn't C# specific, you'll find it in many programming languages. It is received wisdom not a law. One reason is that in practice composition is considered to often win out over inheritance in terms of comprehensibility, implementability and maintainability. It's more common with real world / domain objects to find useful and consistent "hasa" relationships than useful and consistent "isa" relationships unless you're deep in the abstract, most especially as time passes and the precise data and behaviour of objects in code changes. This shouldn't cause you to always rule out inheriting from collection classes; but it may be suggestive.

First of all, it has to do with usability. If you use inheritance, the Team class will expose behavior (methods) that are designed purely for object manipulation. For example, AsReadOnly() or CopyTo(obj) methods make no sense for the team object. Instead of the AddRange(items) method you would probably want a more descriptive AddPlayers(players) method.
If you want to use LINQ, implementing a generic interface such as ICollection<T> or IEnumerable<T> would make more sense.
As mentioned, composition is the right way to go about it. Just implement a list of players as a private variable.

Let me rewrite your question. so you might see the subject from a different perspective.
When I need to represent a football team, I understand that it is basically a name. Like: "The Eagles"
string team = new string();
Then later I realized teams also have players.
Why can't I just extend the string type so that it also holds a list of players?
Your point of entry into the problem is arbitrary. Try to think what does a team have (properties), not what it is.
After you do that, you could see if it shares properties with other classes. And think about inheritance.

It depends on the context
When you consider your team as a list of players, you are projecting the "idea" of a foot ball team down to one aspect: You reduce the "team" to the people you see on the field. This projection is only correct in a certain context. In a different context, this might be completely wrong. Imagine you want to become a sponsor of the team. So you have to talk to the managers of the team. In this context the team is projected to the list of its managers. And these two lists usually don't overlap very much. Other contexts are the current versus the former players, etc.
Unclear semantics
So the problem with considering a team as a list of its players is that its semantic depends on the context and that it cannot be extended when the context changes. Additionally it is hard to express, which context you are using.
Classes are extensible
When you using a class with only one member (e.g. IList activePlayers), you can use the name of the member (and additionally its comment) to make the context clear. When there are additional contexts, you just add an additional member.
Classes are more complex
In some cases it might be overkill to create an extra class. Each class definition must be loaded through the classloader and will be cached by the virtual machine. This costs you runtime performance and memory. When you have a very specific context it might be OK to consider a football team as a list of players. But in this case, you should really just use a IList , not a class derived from it.
Conclusion / Considerations
When you have a very specific context, it is OK to consider a team as a list of players. For example inside a method it is completely OK to write:
IList<Player> footballTeam = ...
When using F#, it can even be OK to create a type abbreviation:
type FootballTeam = IList<Player>
But when the context is broader or even unclear, you should not do this. This is especially the case when you create a new class whose context in which it may be used in the future is not clear. A warning sign is when you start to add additional attributes to your class (name of the team, coach, etc.). This is a clear sign that the context where the class will be used is not fixed and will change in the future. In this case you cannot consider the team as a list of players, but you should model the list of the (currently active, not injured, etc.) players as an attribute of the team.

A football team is not a list of football players. A football team is composed of a list of football players!
This is logically wrong:
class FootballTeam : List<FootballPlayer>
{
public string TeamName;
public int RunningTotal
}
and this is correct:
class FootballTeam
{
public List<FootballPlayer> players
public string TeamName;
public int RunningTotal
}

Just because I think the other answers pretty much go off on a tangent of whether a football team "is-a" List<FootballPlayer> or "has-a" List<FootballPlayer>, which really doesn't answer this question as written.
The OP chiefly asks for clarification on guidelines for inheriting from List<T>:
A guideline says that you shouldn't inherit from List<T>. Why not?
Because List<T> has no virtual methods. This is less of a problem in your own code, since you can usually switch out the implementation with relatively little pain - but can be a much bigger deal in a public API.
What is a public API and why should I care?
A public API is an interface you expose to 3rd party programmers. Think framework code. And recall that the guidelines being referenced are the ".NET Framework Design Guidelines" and not the ".NET Application Design Guidelines". There is a difference, and - generally speaking - public API design is a lot more strict.
If my current project does not and is not likely to ever have this public API, can I safely ignore this guideline? If I do inherit from List and it turns out I need a public API, what difficulties will I have?
Pretty much, yeah. You may want to consider the rationale behind it to see if it applies to your situation anyway, but if you're not building a public API then you don't particularly need to worry about API concerns like versioning (of which, this is a subset).
If you add a public API in the future, you will either need to abstract out your API from your implementation (by not exposing your List<T> directly) or violate the guidelines with the possible future pain that entails.
Why does it even matter? A list is a list. What could possibly change? What could I possibly want to change?
Depends on the context, but since we're using FootballTeam as an example - imagine that you can't add a FootballPlayer if it would cause the team to go over the salary cap. A possible way of adding that would be something like:
class FootballTeam : List<FootballPlayer> {
override void Add(FootballPlayer player) {
if (this.Sum(p => p.Salary) + player.Salary > SALARY_CAP)) {
throw new InvalidOperationException("Would exceed salary cap!");
}
}
}
Ah...but you can't override Add because it's not virtual (for performance reasons).
If you're in an application (which, basically, means that you and all of your callers are compiled together) then you can now change to using IList<T> and fix up any compile errors:
class FootballTeam : IList<FootballPlayer> {
private List<FootballPlayer> Players { get; set; }
override void Add(FootballPlayer player) {
if (this.Players.Sum(p => p.Salary) + player.Salary > SALARY_CAP)) {
throw new InvalidOperationException("Would exceed salary cap!");
}
}
/* boiler plate for rest of IList */
}
but, if you've publically exposed to a 3rd party you just made a breaking change that will cause compile and/or runtime errors.
TL;DR - the guidelines are for public APIs. For private APIs, do what you want.

There are a lot excellent answers here, but I want to touch on something I didn't see mentioned: Object oriented design is about empowering objects.
You want to encapsulate all your rules, additional work and internal details inside an appropriate object. In this way other objects interacting with this one don't have to worry about it all. In fact, you want to go a step further and actively prevent other objects from bypassing these internals.
When you inherit from List, all other objects can see you as a List. They have direct access to the methods for adding and removing players. And you'll have lost your control; for example:
Suppose you want to differentiate when a player leaves by knowing whether they retired, resigned or were fired. You could implement a RemovePlayer method that takes an appropriate input enum. However, by inheriting from List, you would be unable to prevent direct access to Remove, RemoveAll and even Clear. As a result, you've actually disempowered your FootballTeam class.
Additional thoughts on encapsulation... You raised the following concern:
It makes my code needlessly verbose. I must now call my_team.Players.Count instead of just my_team.Count.
You're correct, that would be needlessly verbose for all clients to use you team. However, that problem is very small in comparison to the fact that you've exposed List Players to all and sundry so they can fiddle with your team without your consent.
You go on to say:
It just plain doesn't make any sense. A football team doesn't "have" a list of players. It is the list of players. You don't say "John McFootballer has joined SomeTeam's players". You say "John has joined SomeTeam".
You're wrong about the first bit: Drop the word 'list', and it's actually obvious that a team does have players.
However, you hit the nail on the head with the second. You don't want clients calling ateam.Players.Add(...). You do want them calling ateam.AddPlayer(...). And your implemention would (possibly amongst other things) call Players.Add(...) internally.
Hopefully you can see how important encapsulation is to the objective of empowering your objects. You want to allow each class to do its job well without fear of interference from other objects.

Does allowing people to say
myTeam.subList(3, 5);
make any sense at all? If not then it shouldn't be a List.

It depends on the behaviour of your "team" object. If it behaves just like a collection, it might be OK to represent it first with a plain List. Then you might start to notice that you keep duplicating code that iterates on the list; at this point you have the option of creating a FootballTeam object that wraps the list of players. The FootballTeam class becomes the home for all the code that iterates on the list of players.
It makes my code needlessly verbose. I must now call my_team.Players.Count instead of just my_team.Count. Thankfully, with C# I can define indexers to make indexing transparent, and forward all the methods of the internal List... But that's a lot of code! What do I get for all that work?
Encapsulation. Your clients need not know what goes on inside of FootballTeam. For all your clients know, it might be implemented by looking the list of players up in a database. They don't need to know, and this improves your design.
It just plain doesn't make any sense. A football team doesn't "have" a list of players. It is the list of players. You don't say "John McFootballer has joined SomeTeam's players". You say "John has joined SomeTeam". You don't add a letter to "a string's characters", you add a letter to a string. You don't add a book to a library's books, you add a book to a library.
Exactly :) you will say footballTeam.Add(john), not footballTeam.List.Add(john). The internal list will not be visible.

What is the correct C# way of representing a data structure...
Remeber, "All models are wrong, but some are useful." -George E. P. Box
There is no a "correct way", only a useful one.
Choose one that is useful to you and/your users. That's it. Develop economically, don't over-engineer. The less code you write, the less code you will need to debug. (read the following editions).
-- Edited
My best answer would be... it depends. Inheriting from a List would expose the clients of this class to methods that may be should not be exposed, primarily because FootballTeam looks like a business entity.
-- Edition 2
I sincerely don't remember to what I was referring on the “don't over-engineer” comment. While I believe the KISS mindset is a good guide, I want to emphasize that inheriting a business class from List would create more problems than it resolves, due abstraction leakage.
On the other hand, I believe there are a limited number of cases where simply to inherit from List is useful. As I wrote in the previous edition, it depends. The answer to each case is heavily influenced by both knowledge, experience and personal preferences.
Thanks to #kai for helping me to think more precisely about the answer.

This reminds me of the "Is a" versus "has a" tradeoff. Sometimes it is easier and makesmore sense to inherit directly from a super class. Other times it makes more sense to create a standalone class and include the class you would have inherited from as a member variable. You can still access the functionality of the class but are not bound to the interface or any other constraints that might come from inheriting from the class.
Which do you do? As with a lot of things...it depends on the context. The guide I would use is that in order to inherit from another class there truly should be an "is a" relationship. So if you a writing a class called BMW, it could inherit from Car because a BMW truly is a car. A Horse class can inherit from the Mammal class because a horse actually is a mammal in real life and any Mammal functionality should be relevant to Horse. But can you say that a team is a list? From what I can tell, it does not seem like a Team really "is a" List. So in this case, I would have a List as a member variable.

Problems with serializing
One aspect is missing. Classes that inherit from List can't be serialized correctly using XmlSerializer. In that case DataContractSerializer must be used instead, or an own serializing implementation is needed.
public class DemoList : List<Demo>
{
// using XmlSerializer this properties won't be seralized
// There is no error, the data is simply not there.
string AnyPropertyInDerivedFromList { get; set; }
}
public class Demo
{
// this properties will be seralized
string AnyPropetyInDemo { get; set; }
}
Further reading: When a class is inherited from List<>, XmlSerializer doesn't serialize other attributes
Use IList instead
Personaly I wouldn't inherit from List but implement IList. Visual Studio will do the job for you and create a full working iplementation. Look here: How to get a full working implementation of IList

What the guidelines say is that the public API should not reveal the internal design decision of whether you are using a list, a set, a dictionary, a tree or whatever. A "team" is not necessarily a list. You may implement it as a list but users of your public API should use you class on a need to know basis. This allows you to change your decision and use a different data structure without affecting the public interface.

When they say List<T> is "optimized" I think they want to mean that it doesn't have features like virtual methods which are bit more expensive. So the problem is that once you expose List<T> in your public API, you loose ability to enforce business rules or customize its functionality later. But if you are using this inherited class as internal within your project (as opposed to potentially exposed to thousands of your customers/partners/other teams as API) then it may be OK if it saves your time and it is the functionality you want to duplicate. The advantage of inheriting from List<T> is that you eliminate lot of dumb wrapper code that is just never going to be customized in foreseeable future. Also if you want your class to explicitly have exact same semantics as List<T> for the life of your APIs then also it may be OK.
I often see lot of people doing tons of extra work just because of FxCop rule says so or someone's blog says it's a "bad" practice. Many times, this turns code in to design pattern palooza weirdness. As with lot of guideline, treat it as guideline that can have exceptions.

My dirty secret: I don't care what people say, and I do it. .NET Framework is spread with "XxxxCollection" (UIElementCollection for top of my head example).
So what stops me saying:
team.Players.ByName("Nicolas")
When I find it better than
team.ByName("Nicolas")
Moreover, my PlayerCollection might be used by other class, like "Club" without any code duplication.
club.Players.ByName("Nicolas")
Best practices of yesterday, might not be the one of tomorrow. There is no reason behind most best practices, most are only wide agreement among the community. Instead of asking the community if it will blame you when you do that ask yourself, what is more readable and maintainable?
team.Players.ByName("Nicolas")
or
team.ByName("Nicolas")
Really. Do you have any doubt? Now maybe you need to play with other technical constraints that prevent you to use List<T> in your real use case. But don't add a constraint that should not exist. If Microsoft did not document the why, then it is surely a "best practice" coming from nowhere.

While I don't have a complex comparison as most of these answers do, I would like to share my method for handling this situation. By extending IEnumerable<T>, you can allow your Team class to support Linq query extensions, without publicly exposing all the methods and properties of List<T>.
class Team : IEnumerable<Player>
{
private readonly List<Player> playerList;
public Team()
{
playerList = new List<Player>();
}
public Enumerator GetEnumerator()
{
return playerList.GetEnumerator();
}
...
}
class Player
{
...
}

I just wanted to add that Bertrand Meyer, the inventor of Eiffel and design by contract, would have Team inherit from List<Player> without so much as batting an eyelid.
In his book, Object-Oriented Software Construction, he discusses the implementation of a GUI system where rectangular windows can have child windows. He simply has Window inherit from both Rectangle and Tree<Window> to reuse the implementation.
However, C# is not Eiffel. The latter supports multiple inheritance and renaming of features. In C#, when you subclass, you inherit both the interface and the implemenation. You can override the implementation, but the calling conventions are copied directly from the superclass. In Eiffel, however, you can modify the names of the public methods, so you can rename Add and Remove to Hire and Fire in your Team. If an instance of Team is upcast back to List<Player>, the caller will use Add and Remove to modify it, but your virtual methods Hire and Fire will be called.

If your class users need all the methods and properties** List has, you should derive your class from it. If they don't need them, enclose the List and make wrappers for methods your class users actually need.
This is a strict rule, if you write a public API, or any other code that will be used by many people. You may ignore this rule if you have a tiny app and no more than 2 developers. This will save you some time.
For tiny apps, you may also consider choosing another, less strict language. Ruby, JavaScript - anything that allows you to write less code.

I think I don't agree with your generalization. A team isn't just a collection of players. A team has so much more information about it - name, emblem, collection of management/admin staff, collection of coaching crew, then collection of players. So properly, your FootballTeam class should have 3 collections and not itself be a collection; if it is to properly model the real world.
You could consider a PlayerCollection class which like the Specialized StringCollection offers some other facilities - like validation and checks before objects are added to or removed from the internal store.
Perhaps, the notion of a PlayerCollection betters suits your preferred approach?
public class PlayerCollection : Collection<Player>
{
}
And then the FootballTeam can look like this:
public class FootballTeam
{
public string Name { get; set; }
public string Location { get; set; }
public ManagementCollection Management { get; protected set; } = new ManagementCollection();
public CoachingCollection CoachingCrew { get; protected set; } = new CoachingCollection();
public PlayerCollection Players { get; protected set; } = new PlayerCollection();
}

Prefer Interfaces over Classes
Classes should avoid deriving from classes and instead implement the minimal interfaces necessary.
Inheritance breaks Encapsulation
Deriving from classes breaks encapsulation:
exposes internal details about how your collection is implemented
declares an interface (set of public functions and properties) that may not be appropriate
Among other things this makes it harder to refactor your code.
Classes are an Implementation Detail
Classes are an implementation detail that should be hidden from other parts of your code.
In short a System.List is a specific implementation of an abstract data type, that may or may not be appropriate now and in the future.
Conceptually the fact that the System.List data type is called "list" is a bit of a red-herring. A System.List<T> is a mutable ordered collection that supports amortized O(1) operations for adding, inserting, and removing elements, and O(1) operations for retrieving the number of elements or getting and setting element by index.
The Smaller the Interface the more Flexible the Code
When designing a data structure, the simpler the interface is, the more flexible the code is. Just look at how powerful LINQ is for a demonstration of this.
How to Choose Interfaces
When you think "list" you should start by saying to yourself, "I need to represent a collection of baseball players". So let's say you decide to model this with a class. What you should do first is decide what the minimal amount of interfaces that this class will need to expose.
Some questions that can help guide this process:
Do I need to have the count? If not consider implementing IEnumerable<T>
Is this collection going to change after it has been initialized? If not consider IReadonlyList<T>.
Is it important that I can access items by index? Consider ICollection<T>
Is the order in which I add items to the collection important? Maybe it is an ISet<T>?
If you indeed want these thing then go ahead and implement IList<T>.
This way you will not be coupling other parts of the code to implementation details of your baseball players collection and will be free to change how it is implemented as long as you respect the interface.
By taking this approach you will find that code becomes easier to read, refactor, and reuse.
Notes about Avoiding Boilerplate
Implementing interfaces in a modern IDE should be easy. Right click and choose "Implement Interface". Then forward all of the implementations to a member class if you need to.
That said, if you find you are writing lots of boilerplate, it is potentially because you are exposing more functions than you should be. It is the same reason you shouldn't inherit from a class.
You can also design smaller interfaces that make sense for your application, and maybe just a couple of helper extension functions to map those interfaces to any others that you need. This is the approach I took in my own IArray interface for the LinqArray library.

When is it acceptable?
To quote Eric Lippert:
When you're building a mechanism that extends the List<T> mechanism.
For example, you are tired of the absence of the AddRange method in IList<T>:
public interface IMoreConvenientListInterface<T> : IList<T>
{
void AddRange(IEnumerable<T> collection);
}
public class MoreConvenientList<T> : List<T>, IMoreConvenientListInterface<T> { }

Repurposing the .net type system - bad idea?

I'm playing around with writing an item crafting system that I might want to put into a game someday. There are Recipes which specify the ingredients they require and what they produce.
I wanted the recipes to be flexible, such that they only required a broad category of ingredients, not an exact one. For example, a recipe for a weapon blade might just say it requires a metal, not specifically steel. The recipes have to verify that the ingredients given are within the acceptable category. Some materials might belong to multiple categories.
Then I had a possibly brilliant, possibly insane idea. The .net type system already implements that! So for each material, I add a property of type Type, and use IsAssignableFrom to verify the ingredients' compatibility.
I have a file that looks like this:
public interface ItemType { }
public interface Material : ItemType { }
public interface Metal : Material { }
public interface Gold : Metal { }
public interface Silver : Metal { }
public interface Iron : Metal { }
public interface Steel : Metal { }
public interface Wood : Material { }
public interface Coal : Material { }
And so on. None of those are ever implemented. I'm just borrowing the built in type checking for my own purposes.
Is there anything necessarily wrong with this?
edit: actual question
If I've been clear enough to explain what I'm trying to accomplish here, then what would you suggest is a good way to go about it, ignoring this whole type system abuse thing? Would you have also used this solution, or something else?
Second question, are there any pitfalls to watch out for in what I've done here?

Is there anything necessarily wrong with this?
Yes, everything.
Classes and interfaces are meant to express behavior. There is no behavior in your code. Your code is not miscomunicating the intentions. Usually, when you see interface, you expect it to have some method and that method is called. That is not the case here.
It will become impossible to define the materials and recipes in some kind of configuration/resource file, like most normal games do. So you have to recompile every time you want to change the materials or recipe a little.
It will become problematic to create items/materials that are somehow related. For example, lets say there are multiple tools and each tool can be from different materials. In your case, you have to write down every combination. In ideal case, you can just run few nested for loops which create each combination.
You cannot parametrize the materials in any way without creating classes of them. For example, you might want different colors of wool. How would you do it? Create interface for each color? Or use some kind of enum as parameter. But you have to create class for that.
Better way would be simple Item class that has collection of tags. Even simple strings should be enough.

Design Pattern For Persistence

I am working on a project where I am wrestling with trying to move from one persistence pattern to another.
I've looked in Patterns of Enterprise Application Architecture, Design Patterns, and here at this MSDN article for help. Our current pattern is the Active Record pattern described in the MSDN article. As a first step in moving to a more modular code base we are trying to break out some of our business objects (aka tables) into multiple interfaces.
So for example, let's say I have a store application something like this:
public interface IContactInfo
{
...
}
public interface IBillingContactInfo: IContactInfo
{
...
}
public interface IShippingContactInfo: IContactInfo
{
...
}
public class Customer: IBillingContactInfo, IShippingContactInfo
{
#region IBillingContactInfo Implementation
...
#endregion
#region IShippingContactInfo Implementation
...
#endregion
public void Load(int customerID);
public void Save();
}
The Customer class represents a row in our Customer Table. Even though the Customer class is one row it actually implements two different interfaces: IBillingContactInfo, IShippingContactInfo.
Historically we didn't have those two interfaces we simply passed around the entire Customer object everywhere and made whatever changes we wanted to it and then saved it.
Here is where the problem comes in. Now that we have those two interfaces we may have a control that takes an IContactInfo, displays it to the user, and allows the user to correct it if it is wrong. Currently our IContactInfo interface doesn't implement any Save() to allow changes to it to persist.
Any suggestions on good design patterns to get around this limitation without a complete switch to other well known solutions? I don't really want to go through and add a Save() method to all my interfaces but it may be what I end up needing to do.

How many different derivatives of IContactInfo do you plan to have?
Maybe I'm missing the point, but I think you would do better with a class called ContactInfo with a BillTo and a ShipTo instance in each Customer. Since your IShippingContactInfo and IBillingContactInfo interfaces inherit from the same IContactInfo interface, your Customer class will satisfy both IContactInfo base interfaces with one set of fields. That would be a problem.
It's better to make those separate instances. Then, saving your Customer is much more straight-forward.
Are you planning on serialization for persistence or saving to a database or something else?
Using a concrete type for Customer and ContactInfo would definitely cover the first two.
(A flat file would work for your original setup, but I hope you aren't planning on that.)
I think it all comes down to how many derivatives of IContactInfo you expect to have. There is nothing wrong with a bit more topography in your graph. If that means one record with multiple portions (your example), or if that is a one-to-many relationship (my example), or if it is a many-to-many that lists the type (ShipTo, BillTo, etc.) in the join table. The many-to-many definitely reduces the relationships between Customer and the various ContactInfo types, but it creates overhead in application development for the scenarios when you want concrete relationships.

You can easily add a Save() method constraint to the inherited interfaces by simply having IContactInfo implement an IPersistable interface, which mandates the Save() method. So then anything that has IContactInfo also has IPersistable, and therefore must have Save(). You can also do this with ILoadable and Load(int ID) - or, with more semantic correctness, IRetrievable and Retrieve(int ID).
This completely depends on how you're using your ContactInfo objects though. If this doesn't make sense with relation to your usage please leave a comment/update your question and I'll revisit my answer.

Designing classes in c#

Suppose we want to model a doctor's patient: a patient has a prescription history, an appointment history, a test results history... Each of these items is itself a list.
What's the best way to create the patient class?
class MyPatient{
List<Prescription> Prescriptions {get;set;}
List<Appoints> Appoints {get;set;}
...
}
class Prescription{
string PrescripName {get;set}
int Dosage {get;set}
}
class PatientAppoint{...}
This is what I have in mind; please let me know if you have some suggestions.

There are a lot of things to take into account when designing your classes:
Inheritence vs Composition -- Use "Is A" and "Has A".
For example, a Car is a Vehicle. A Car has a Engine.
Don't throw in a bunch of junk into a class to try to make it work for another class.
For example, if you want a Prescription history you'll probably need a Prescription and a Date. But, don't throw a Date into Prescription if it doesn't fit in, instead, extend it to a new PrescriptionHistoryItem class which inherits from Prescription.
Start off with an abstract representation or contractual representation and build off of that. You don't need to end up keeping any abstract classes or interfaces if they are unnecessary, but they might help you on the way there.
Basically, there are a lot of things to consider and this question is pretty open ended. There are way too many design patterns and topics to consider and that are debatable. Overall, your class hierarchy/design looks fine though.

Instead of keeping all classes in a file , i would create a separate file for each class with the same name. It will be easy for future programmer to debug or it will be very clean to understand.

Yes, that is a pretty standard way of representing those objects in OOP. Your patients have a one to many relationship with both prescriptions and appointments, so you patient class has a collection of each. You may want to keep how you are going to persist you data (database I assume) in mind as you design your class structures and layout.

This is a good example of where the model can become problematic at runtime. As you start to draw this out, you may end up with a collection of patients at somepoint. If you have data adapters building patients, and stuffing the prescription, visit, test, etc. histories into the patient classes, then a collection of Patients can end up being quite large. Now if this large collection is being transported over a network, say, between a WCF service and a client, it could become burdensome. For example, if you are just displaying a list of patients...
So in my opinion, I would look at the system from a slightly higher level, and consider some of the things I mentioned above. If you are going to be passing around collections with 500 patients in them, then I might consider a model that allows me to associate patients and "item" histories when necessary, but also be able to have them separated when desired...
This would affect the model, in my opinion, because I don't like to design a class where when the data adapter builds the instance, the population of fields is arbitrary, that is, sometimes it populates them sometimes it doesn't... But I have done that before... ;)