Your first project can be a game, and it can be a good experience, but keep it simple.
Ignore menu systems, fancy graphics, 3D rendering, networking etc. until you really get the hang of things.
Of course you need a few "hello world" programs to get your toes wet, but after that try to make things fun.
Everybody says to start out by making pong, but honestly that's nothing new and no fun to play when your done, right?
Make something new, but with the same simplicity as pong.