A Debian-based distribution is probably the best choice, IMO.

The *ubuntus have lots of good points, but they don't install proprietary things like Flash by default. (It's relatively easy to do by selecting the appropriate repositories, https://help.ubuntu....RestrictedFormats .)

Linux Mint is an offshoot of Ubuntu which has a lot of fans: http://www.linuxmint.com/about.php It also doesn't include proprietary drivers, though.

If you don't want to have to worry about customization, then OpenSUSE and others are good choices, but they aren't Debian-based.

Puppy Linux has lots of fans, too, it's very compact. But the GUI may be a little too child-like:
http://www.puppylinux.org/home/overview

Popularity-wise, you're probably best with *ubuntu and perhaps something based on RedHat/Fedora.

Good luck.

Cheers,
Scott.