While MAME may not require a monster computer for the classics, I got fed to the teeth with Windows-98 and tweaking things to run optimally on an older 400MHz machine. It really needed more RAM and a video card. So instead of putting more money into that...
I just built a very nice 2GHz machine for $360 with an nForce motherboard, great nVideo graphics, onboard sound, S-video out, etc. While it's totally overkill for right now, I think it'll be great for any cabinet friendly game, other emulators, general DVD/jukebox use, and other things too. It'll last more than a year or two too. And I can finally run Emulaxian!
Anyway, my point here is that if you have a little money, I personally would not bother trying to save $50-$100 to get a PIII class machine and run Win98 when you can build a mainstream PC running W2K/WXP that'll do more and go further in the long run. The driver management and other OS features alone makes it worth it to me. And you can use cheaper/used components and build less nice of a box (but similar in capability for $250-$300.
That said, I had to assemble it so you need to know a little something about PCs. You may be better off with a TigerDirect or eBay used or no-name brand. But I'd still suggest you avoid the PIII/Win98 route no matter what you do.
My opinion anyway. YMMV.