Isn't C# the newer version of C++ therefor making it basically the same thing?
No they are completely different and unrelated.
What you're trying to do will make a big difference.
This summer I've been having an internship at Fedex and they use a TON of Java. I've fallen in love with the language. If you're making general purpose apps I'd highly suggest Java.
The only reason I might suggest C# for game development is because it's much more common and you'll find better support. C# with XNA makes it really easy to make something. Java does have graphics libraries but you probably will take slightly longer to get off your feet.
To those who are suggesting Python, yes that's a great language too but if you end up making some big complex system, you're probably going to want Java or C# for their object oriented features.