I think ubuntu is probably one of the easiest linux distros to start out with. Their software repositories are kept fairly up to date, and don't require a user to compile new software. There is also a lot of help on the internet for ubuntu. The newest version also added support for Compiz (which is the "cool desktop accelerator" that makes things pretty). That being said, I think Sabayon Linux it a very cool distro to try out. They have live DVD full of games, browers, cool 3D effects, and the best part of all: nVidia and ATI drivers built in.
http://www.sabayonlinux.org/ for the most part everything works out of the box. The live DVD is fun to play with, and it comes with Gnome, KDE, Enlightenment, and some other. If you don't know those are all desktop management systems, once you play with them you will understand more.
Good luck and I hope you enjoy.....