I am in the long process of putting together a cabinet, and the computer I am using right now for testing my control panel connections is pretty similar.
I'm using an AMD K6-166, 64 MB RAM, 8MB Vid card. I have no problem playing most of the classic games in Win98 using MAME 0.60. I didn't want to mess with setting up all of the DOS drivers since an upgrade is planned in a month or so.
Some of the games that play no problem include: Ms. Pac Man, Frogger, Donkey Kong (& Jr), Galaga, Centipede, Track and Field, Kangaroo, Qix, Robotron.
The only thing of that vintage that I have had trouble with is Asteroids, but I think that game is known to require more power to emulate than other 70s and 80s games.
Also, you might want to check out an emulator called Vantage. I don't know much about it, but it was recommended to me for low powered systems.
If you do get around to doing a cabinet, I have found the Happs Universal to be a pretty decent four way stick. Not quite a ball-top, but not bad and has a similar feel to the short-throw sticks of old.