MinGW compiler

Does anyone know which files I would need to download in order to use the compiler?

http://sourceforge.net/projects/mingw/

I'd suggest you download dev-c++.
It includes the mingw compiler, but it does so as a handy single executable which takes out all of the guesswork.

mingw is a small package of libs. the compiler is gcc
if you want to do full posix programming you'll have to use Cygwin