Assuming you want to play older games...
Any of them will work, but don't bother with the NVidia FX series. The 6-series will be much better in every way. A 6600GT should not be hard to come by, and runs cool enough that it should still be alive. A 6800GT might be, too, but expect one of those to be loud.
You can also get a Radeon 9800XT. The 9800 PRo is hotter and slightly slower. No point in bothering, if an XT is available. If going for older games, the Radeon 9800XT would be what I would pick (FYI: I have just such an old XP box with a 9600XT in it).
Running Windows XP, you get your choice of drivers. Older drivers, from times when the cards were current offerings, will tend to be optimized better for them, while newer drivers will be more compatible with newer games.
On the Radeon side of things, if you run XP, you can use ATI Catalyst drivers, which will tend to be fast but flaky, or AMD Legacy Catalysts drivers, which are pretty solid, but performance may not be the best (they've been crash free for me, support the TV outs, and play most old games OK, which is good enough for me!).
If it is a run of the mill office type computer, however, you should just get a brand new card, like that Radeon HD 4xxx, for video offloading and such (better yet, a 5xxx series card). There's a chance that it may be quite fast in games, as well, compared to the older ones, but performance seems to be a crapshoot with new GPUs on AGP bridges.
