Unity is good. You can use either javascript(unityscript), C#, or uhmm boo or w/e it's called, to script in it.

This is a lie. Using gamemaker is like trying to build a beautiful house with a butter knife and a pile of baked horse shit.

I'm currently attending a college that offers technical-oriented majors in game design, coding, entertainment design, etc, and if you can get one coding language down cold, like C++, you'll be ahead of the curve.

I would also recommend learning a highly object-oriented programming language like javascript, since it's extremely prevalent, and gaming in general is moving further into an online medium. Also javascript is a lot easier to pick up than C.

Or you could learn Flash's Actionscript, create some flash games, and then release a mind-blowingly innovative new game based on your creations, make many millions of dollars, and become the next Notch, ala Minecraft.
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Artists are the blue collar workers of the game industry, and are paid as such.

Programmers are white collar.

Game designers are the fat hairy guys in dirty clothing who get paid almost as much as the programmers to do a job most teenage boys could do better.