I would recommend Xubuntu. It's based on Ubuntu (probably the most popular Linux distro currently out there) but games with xfce instead of GNOME, xfce being lighter on resources. You may also try the xfce version of Linux Mint, but personally I just hated it... the GNOME version of Mint is excellent, though, but for a computer with specs as low as yours, I definitely would not recommend it.
PC eye already gave a fairly comprehensive list of distros you may try, though a few of then (DSL and Knoppix for example) are better suited to run off LiveCD, and if Gentoo is more of a thing for an advanced user so if you're a Linux n00b you'll probably want to steer clear of it.
If you're willing to so some research on your own, look for distros that come with JWM, Fluxbox or xfce desktop environment instead of GNOME or KDE.