I normally use CopyWipe v1.14 (included in the Ultimate Boot CD
), which is also available as a standalone DOS-only image
that you can write to a floppy. I've used this to wipe hard drives on an 800 MHz VIA C3, as well as a PIII 500, and a P3 300, so it should work pretty well for your purposes. When you wipe you only need to do one pass of zeros, and it won't take nearly as long as some of the other wiping options. I'd give it overnight if it's a somewhat large drive and a slow PC. If it's taking absolutely forever (stuck at 0%), or if it gives you a read error, then your hard disk is probably dead.
As for the operating system, if you've got at least 192-256MB of RAM, you could run a minimal Arch Linux install quite well, with a lightweight window manager like Openbox or Fluxbox, though Arch is not really a beginner's distribution. Xubuntu and Lubuntu both would likely work quite well on such machines, provided you have sufficient RAM, probably about 256MB would suffice for either. In my experience, Lubuntu can run on quite low-end hardware and run quite well. Lubuntu's minimum RAM would be about 128MB, but 256 should yield at least tolerable performance.
Let me know how it goes with CopyWipe and the OS install, I'm happy to offer more help as you continue your project.