Probably the best reason for using Linux is to utilise your old hardware. If you have never installed Linux before, then you may want to read up a bit at http://www.linuxdoc.org
for some specific info on problems which may arise.
Mandrake is a very good newbie distro (well it served me well!), and the 7.2 version is up to date with most things, if not all. However, I dont know how good it is on a low spec machine, because I use Mandrake on my suped up windoze machine. Maybe someone else can tell you there.
You will definately want at least 32megs of RAM for your distro.
If you feel really adventurous, and you sound like you have another comp, then you may want to install smoothwall and set up a server on the old comp. Its just a suggestion.
I hope you have fun and enjoy your Linux OS!