There are websites around where it asks you some questions about what it will be used for and how much technical knowledge you have and then tells you which distros would be best for you.
I would go ubuntu for starters, and if you want to get to understand linux, try to do as much as possible via command line rather than the GUI.
I'm personally quite happy with Ubuntu and most of the computers in my house have some version of ubuntu on them: I have two htpcs running xbmc live, a desktop and a laptop running ubuntu lucid (the desktop is dual boot with windows 7 because there's still some stuff I need windows for), and a server running ubuntu server edition. I'm trying to convince my girlfriend to switch to ubuntu as well.