>> What OS should I install if we get 512 MB? Or 1 G? I'm guessing at some point I would be limited by the processor speed, and we're not really looking to replace that. We just want it to do basic things, like type and access the library's wireless.
It's kind of unlikely that you'll be able to fit more than about 128Mb ram in a 1998 laptop. PC compatible gear just didn't have the kind of capacities that you're used to with current gear. I hope I'm wrong, but even if I'm not it might be an uphill struggle to source the memory (not compatible with current strains).
At the risk of uttering heresy, Windows NT4 would run acceptably in 32Mb, and was a little more together than Windows 85, although I don't remember if it had USB support. Incidentally, the USB support of the time was nowhere near as fast as the current USB 2.0 standard. Personally, I'd treat this is a project you'd do out of interest, rather than to get a functional laptop out of it.
Having said that, if your friend can handle a command line, it'd be usable for basic text editing, and you can even browse the web in a limited fashion using text-only browsers. Plus point: your chances of getting any kind of virus are almost zero.