The features you have listed can be split into a couple of categories, firstly there are the features that are purely syntactical sugar, they don't allow you to do anything new, they just help you write cleaner code that is easier to read. The features fit in this category are:
- Object Initializers (avoid overloaded constructors, or many lines of initialization code)
- Extension Methods (neater way to access static methods in helper classes)
- Lambda Expressions (when used as a replacement for delegates)
- Anonymous Types (replace small, throwaway classes in certain circumstances - mainly used to support LINQ and not often used in your own code)
Two of the other features actually provide you a programming benefit which may improve the performance of your application
- Generics (helps avoid boxing on value types)
- LINQ (when used to defer intensive queries until a more suitable time (IQueryable))
But the main power of LINQ is as an integrated query language, allowing simple, type safe methods for querying datasets (a database, XML, objects etc) in a more OO less SQL way.
Therefore there is no great advantage in forcing yourself to use the first three. Personally I think they are all good things to get into the habit of using, but you won't see any major benefit from them if you don't like the syntax or find them unnatural to use. If you do want to use them then code style plugins such as Resharper or CodeRush will have features you can turn on to warn you when you could use the new style instead of your longhand code.
You can start using generics by relying on the supplied generic collections rather than the old .NET 1 lists and arrays. There are cases where you will want to write your own generic classes, but you should have a good handle on them by the time that happens if you start leveraging the supplied ones now.
LINQ will either be fantastically useful to you or completely pointless, depending on how much data you access, if you think you'll need it I'd suggest looking at LINQPad - it gives you a very nice sandbox to play in where you can get a feel for the way the language expresses concepts. You'll either love it (most do) or see no reason for it in your code.