Basically, you have to start with what do you WANT to DO with your new computer... Are you willing/wanting to LEARN or do you want to turn it on and have it "work" like windoze . . .
What hardware do you have? If your camera/scanner/printer, etc wont run with linux, then you are stuck with buying new or running an OS that will work with them...
If you have a NEW computer though, then your stuff should still work with the OLD computer...
see :
http://www.linux.org/lessons/beginner/toc.html for one beginners section...