Comment How About FreeBSD? (Score 2, Informative) 507
You can still download floppies for a FreeBSD Net Install. Assuming your network card works with the drivers on the boot floppies you should be able to do a base system net installation of FreeBSD and then build whatever else you need from the ports tree afterward (or install the binaries from the packages collection. Should make for a small, clean installation with only what you need and nothing else to take disk space or consume your limited resources.