The lowest you can use is a 386 and 8 megs of ram. But that would be a pain and none of the newer distros would run on this (apart from slack but that's coz slack is cool

).
Linux will work on both those machines though the cyrix will be slow (and i can't remember if there was something dodgy with those chips that need a workaround in the kernel).
I have a pentium II 233 in my room which happily run windowmaker, kde, gnome.
Just make sure you look at the numerous posts on this forum about making linux go faster (search for linux and slow).
HTH
ALex