A game designer writes the plot, or storyboard, or just draws how things should work.
A game developer takes the design and art from the art department and uses code to make everything happen.
Do you want to design games or develop games?
Do you want to work on small things, like iPhone games? Large things, like console RPGs?
If you want to design games, start designing games of all types. Build up a cache of ideas. Go from there.
If you want to develop games, you can download the XBox game studio for a low monthly fee. Same with the iPhone one. The PS3 is reputedly a pain in the @ss to develop for, and I'd ignore it. I'd focus on C++ first, and perhaps (later) pick up C# (XBox XNA) or Objective-C (iPhone Cocoa). If you wanted to use a scripting language to build upon a game engine someone else has already built, Lua is popular, but that assumes you have that game engine to run the darn scripts.
If you already have any degree, you'd probably be much better served by either just taking the very minimum of classes necessary, or self-teaching this one. Hands-on experience just *doing* this will be more useful than formal education.