The 2012 Mac Mini's are listed on this article. Can I run windows 7 64-bit on it and/or the 32-bit?

I would buy nothing less than Windows 7 64-bit Pro.

32-bit only addresses 3.5 GB RAM ... 2012 Macminis can hold 16 GB.

64-bit Home addresses 16 GB RAM.

64-bit Pro addresses 192 GB RAM and han an XP mode.

This is all about having a good version of Windows for future use. Yu can buy "Syem Builder" version of 64-bit Pro for $140.

Not if you need something in Ultimate that is not in Pro.

Compare for yourself: http://en.wikipedia.org/wiki/Windows_7_editions