I made a game for a class two years ago (I was 18 too at the time) and we made it in C#. While I observe that large C# programs usually operate slower than large C++ programs, C# also requires much less work on your end. Memory management is done automatically, and for the scope of a first game, it's plenty fast enough. (Our game is a full-fledged 2D multiplayer Starcraft-like RTS.)
I'd root for C# as it should be easier to manage. However, if you want to become a professional game developer, just remember that it works only on Microsoft platforms. (Still, C# can be a good stepping stone to C++, and if I had to relearn the two languages, I'd try to learn C# first.)