What operating systems are compatible for the different platforms of computer?

Depends on what kind of hardware you are starting out with first off. If you have a macbook or powerbook, you can run Mac OS X with no issues. If its a powerbook, you're pretty much stuck there unless you want to try ppc Linux which I've never been fond of. If its a macbook (has an Intel processor) you can put any flavor of windows on it, any Linux, pretty much what ever you feel.

If you are starting out with a PC laptop or desktop, your simplest bet is a flavor of windows. If you have a fairly new computer, hop on Windows 7, its not great but beats the hell out of vista any day. You also have the option of a Linux distribution (ubuntu, suse, kubuntu is the best from my experience). And if you really want to play around, you can even put OS X on your PC but you'll have to Google around for that one, not sure if answers.com would condone talking about that here.