Here's a bizarre scenario. I have a fully working 486DX system that has been sitting there unused for the past 5 or so years. Here are the specs:

Processor: 486DX 66MHz
Motherboard: Damned if I know, something with a riser card, AT-style. I'm guessing LPX-based or NLX-based
Ram: 8 or 16mb, I'll check soon
Hard Drive: 500mb currently fat16
Current OS: Windows 3.1 for workgroups
Ethernet adapter: None installed and it's only got ISA slots
Modem: Yes, but Imy ISP is cable so it's mot much use. Only like a 28.8 anyway.
Floppy: Yes
CD-ROM: 4X

Age: 10+ years...

What distro would fit on the hard drive and actually work on this ancient thing? Windows3.1 runs fine...

go to Linux.org and there you can choose minimalist installations. You can also go to Linuxiso.org and search around there for some more ideas.

What do you want to do with it?

The best thing I would say is turn it into one of the best routers you can buy,especially since you have broadband, and thats not very secure.

Use a distro like Smoothwall, clarkconnect, or IPcop.

Theres lots of threads on it.