Whichever one is available at http://fedoraproject.org/get-fedora at any given time, preferably a live image. Download an ISO image, burn it to disk, and then reboot — when your computer boots from the optical drive, you can take it for a test drive without losing anything on your hard drive, and if/when you’re ready to make the jump, you can do a full install from the same disk.
Personally, I find it’s a great way to make older hardware usable — Windows may run like a dog, but Linux will still be pretty snappy. And if all you want is a web browser, email, and some lightweight office stuff, old hardware works like a champ.
Except for Flash. But Flash is evil.