RedHat or Mandrake for legacy systems
I used to run RedHat on a system similar to that. Worked great with WindowMaker as a window manager. Just had to make sure not to overload with too many programs running. Since there is no personal RedHat now, I guess use Mandrake, just be careful on the install (It likes to install a lot of stuff you don't necessarily need on an old PC.)
I would definitely avoid running GNOME or KDE. They will run, but you will lose a lot of processing power on a 300 MHz PC. Also, you can always tweak the kernel to work better for that processor, but if you've never done it, you might just wait until you have some free time and a spare PC to work with.