Hey Josh,
There are dozens of tools out there for cheap or free. I used WebMatrix a
couple years ago. It's more for Web programming than games but is one
example of many such options. A couple hours on Google can find a lot more.
Do a search on free compilers or free IDE (interactive development
environment) and start clicking.
As far as the differences between .NET and "standard" languages is a
combination of marketing and all the services behind the language. From a
standpoint of "how do I write a program", .NET is essentially just another
modern language. You've got variables and classes and objects and
statements and... What makes .NET different from earlier languages is what
it's built on. There's a huge amount of prebuilt functionality. For
example, there are some objects for dealing with files and folders that make
what used to take five commands now takes two. There are a lot of other
advancements, but from a standpoint of how to write the programs, I'd say
that's the biggest.
C++ is probably a solid choice not only for game programming but for
programming, in general. It does what most mainstream languages are
expected to do and lets you get into details that many other languages
won't. It's interesting that (I think) three teens have responded and two
of you have said you want to get into game programming--and #3 didn't say.
You may find that almost all of the fun is in solving the problem, not
playing the game in the end. If that's the case, you may just a future in
programming. That's another selling point for C++ since it and similar
languages (like Java and C#) are used very widely. If two out of every
three new programmers want to write games and one out of every 1000
programming jobs is in game development, you might want to work out that
math...
Good luck,
John