Ubuntu 11.04
I would agree that you start with debian, but as you become your familiar I would move to debian. Ubuntu tends to take control from the user so that you can't "break things," but this causes some limitations I can't stand. Having to use sudo naudilus to open up a root file explorer, and sudo bash/dash because su doesn't work also annoys me a bit.
Ah that was actually supposed to say I agree to start with Ubuntu .
I am very impressed with Ubuntu 11.04. It blows me away how fast and how stable it is! I use my computer for video editing and processing as well as the standard stuff like spreadsheet number crunching and word processing. So far, I've dual booted my two desktops (still need Windows to run games) and installed Ubuntu exclusively on my notebook computer.