Does your ‘old’ computer support booting from CD?
If so, then Mepis, or regular Knoppix, or any of a dozen other ‘LiveCD’ variants will work.
If not, any small hard drive (3-4 GB) will hold a complete distribution.
**Not a plug**
I recommend a book with distro if you have never used Linux before. Either ‘Master Linux Visually’or my new favorite ‘Point & Click Linux!’ by Robin Miler.
Good Luck and welcome the world of diversity.