Try vector linux:
Minimum system requirements: 386 processor, 16MB RAM, 350MB disk space.
This isn't really a "mini" distro from what I can see. You get a fast, slimmed down graphical desktop(icewm) which you will need. There's no way your hardware will run kde or gnome. There's also a pretty full set of tools with which you can explore linux. The distro has been optimized with older hardware in mind to give a servicable linux desktop experience. If you could find some compatible ram in an old box somewhere, that will help performance greatly.