I want to be a game programmer too :D
So, first, no Java.
Second, C++ would be the best choice to make games, C# is used in some scenarios, but I wouldn't recommend to start with that. I started with C to learn the basics easily, and my teachers say that with that basis I will be able to understand the other languages more easily. But any language you decide to start with, I would say relax, don't hurry to make games, or think your first class or something you will be making a game or something. It's important to learn everything with calm.
So, going back to the question, if you are really crazy for results haha, you can start with C++, but if you want a strong basis, C. Alongside these, you can use programs like Game Maker not to learn how to program, but to understand the logic that a game requires and stuff like that. Don't expect too much of the games you make with these programs, but just try to understand the concepts behind them.
But I will say it again, it will take some time to start making games. You will start with basic operations, math problems and stuff like that, but don't think these are not important! They are essential for any program, although in the beginning it is very difficult to notice that.