If you choose to derive List<>, the most evident drawback is that your user can't "guess" which method is overriden, and which ones is provided "as is". List is very rich class, especially when extended with LINQ, and a custom overriding of it can quickly be misleading and bug prone.
If you would like to provide List "as is", with a few custom methods, Extension Methods for List (where you target your specific kind of "T" !) could be really helpful and allow to preserve the original behavior of List.
Users will enable and use your Extension Methods only if they need them.
The drawbacks are the evident ones of Extension Methods : you can't do everything you want in them. There are plenty informations on web on Extension Methods.
IHMO the best thing to do is to encapsulate the List (or other enumerable) in your own class. Of course, T is specific to your own case.
The drawback is the need to redefine all relevant methods. Of course you can also expose the inner list (or, better, a Read only copy of it) with a specific property to allow user to directly use it. Your class can also implement IEnumerable.
Please also note that there are already tons of useful rewriting and extending methods and full custom collection implementation to improve List and other collections types on the web, and in Framework itself (most of collection types are misused, and LINQ adds a lot of good things). Take care to not reinvent the wheel.
