The first thing you need to do is to check the distrowatch popularity list. http://www.distrowatch.com
. This list ranks many distributions by the number of hits the site gets per IP per day. They may not necessarily be ranked by which distro is best, but distro popularity could be important since using a more popular one can get you more help.
Pick one of the top 10, giving precedence to those that offer a live/install cd. This will let you try out a distro in a live environment before you install it.
When choosing from the top 10, you can safely include any derivative of Ubuntu such as Kubuntu or Xubuntu, even if not in the top 10, since the main difference is in the desktop gui.
If you have time and like to experiment, try several distros and pick your favorite for your permanent installation.
The best technique is to just jump in and try it, then ask here for help when you get stuck with something. It's usually a good idea to try the docs first, because figuring something out yourself helps you learn MUCH faster. Try the tutorials on this site, or at http://www.tldp.org/