jester83,
A GNU compiler would be sufficient to learn C++. Heck, if you do some searching, I'm sure you could find a C++ compiler for free (unix-based systems all come with one... but that won't help a windows person). Google for it... see if you can find a compiler for free. If you get really serious with it, you might want to consider buying an IDE such as MS Visual C++. There are added features that can make development a lot easier than the command-line compilers.
If you're just learning the C++ language, let me warn you... Game programming is not for the faint of heart. Don't think for a moment that you're going to be writing a solid Quake/HalfLife engine right off the bat. For a long time, you will probably be writing games like tic-tac-toe and Blackjack in order to (a) learn the syntax of the language and (b)learn the logic behind games.
I know that sounded bad; don't get discouraged though... it can be done, you just have to be willing to stick with it. Just make sure you have realistic expectations.
You should definitely spend some time reading posts on sites like this one... I've learned a bundle in the last 2 years. Good luck!
Ben
There's no place like 127.0.0.1.