I think Slackware is one of the best distributions to use in a situation
like this, although it might take a bit more user knowledge to get it set
up.
Also, Slackware I think still comes with boot and root disks so you can
get it up and running with floppies enough to either do a CD-ROM or
network install.
Even modern distros aren't _that_ bad on older machines. I am typing this
on a PII-400MHz with 128MB of RAM that I use as my primary desktop here at
work. I'm running SuSE 9.1 (I haven't upgraded the OS recently because
the machine has no CD-ROM drive) with full KDE and a lot of konsoles and
firefox running locally... and while it bogs down sometimes, it's
perfectly usable.
Though my first Linux box was a 486-66 with 20MB of RAM and a 200MB
hard-drive (which I ran enlightenment and Netscape 3 on) so by comparison
anything else seems pretty zippy.
Vince