You can use Slackware with XFCE or one of the smaller window-managers on that machine, in fact you should be able to use any distribution, if you choose a lightweight desktop environment, like XFCE, LXDE or Enlightenment. Alternatively you can choose to use a window-manager instead of a desktop environment, like IceWM, FVWM, JWM, one of the *boxes or a tiling WM.
My choices would be Slackware (XFCE or a WM), Debian (XFCE, LXDE or a WM), Xubuntu or Lubuntu (XFCE or LXDE), Vector (XFCE or a WM) and antiX (IceWM or Fluxbox).
There are more, this were just a few that came into my mind first.
EDIT: I will not recommend Puppy Linux here to learn Linux. It is not a multi-user distribution and therefore you always have to run it as root. This way you will not learn enough about user permissions, and also are permanently in danger to damage the installed system.
Last edited by TobiSGD; 07-26-2011 at 10:14 AM.