(Stock caveat: I Am Not A Lawyer and this should not be construed as specific legal advice.)
If all you're concerned about is that your work is copyrighted to you, then you're in luck - that happens automatically upon creation of the work, and no explicit copyright mark is needed.
On the other hand, if you're concerned about the prospect of people infringing on your game's copyrights (and you're in the US - other agencies will be appropriate for different countries, of course), then probably the simplest route to take is registering your copyright via the US federal government's Electronic Copyright Office; this provides all the benefits of classic 'paper' registration for a relatively nominal fee (it looks like $35). This allows several benefits over the implicit copyright that's automatically granted to your work; for instance, you must register a copyright on your work before you can file a suit for infringement (though note that you don't have to register before learning of the infringement!), and having registered in advance of any suit both provides prima facie evidence of your copyright's validity and allows you to recover attorney's fees and statutory damages for the infringement. (For more details on this, I recommend ask.com's page on copyrights or the SFWA page on the benefits of copyright registration)
If you're very concerned about people infringing on your IP rights, or you want protections beyond just basic registered copyright protection (e.g. trademarks on certain expression elements or on a logo, etc), then the answer starts with 'Find An Intellectual Property Lawyer' — they'll be much more competent to advise you than anyone else here.
Separate from both of these matters, of course, is the issue of how much you should be concerned with copyright protection right now. I won't tell you not to be worried; that's an issue you can only resolve for yourself. But I will say that my gut instinct is that you should be much more worried with making your game first; having to be actively worried about people stealing your code falls into the Nice Problem To Have category. That's not to say that you won't have it eventually — just that IMHO it should be quite a ways down your list of concerns.