Okay here we go.
Doom III is a purely OGL game, thusly, will run great on nVidia cards as their OGL implementation is better. That alone is enough of a reason to go nVidia (sadly), because the Doom III engine many people suspect is going to take place of the Quake 3 engine. ALSO, the 6800 ULTRA is a great card for the price.
The ATi X800 Pro and XT, however, outperform the GeForce equivalents (by whatever slim margins) in every testing, unless they're biased. The X800 Pro more than outperforms the 6800 non-Ultra. The XT slimly outperforms the 6800 Ultra.
If you're going for budget cards, I'm going to suggest three cards for you. 9800 Pro--220 I believe? 250 at the max. Great card, wonderful for all of today's games and really good for all of tomorrow's. 9800 non-pro--200 or less. Basically a somewhat slower performing 9800 pro, can't boost the AA or AF up as high, but still a good card. 9600XT 140-160 dollars. GREAT card for the price, basically THE budget card to have nowadays.
These cards are all made by ATi, and I'll suggest some manufacturers for you. Sapphire, Visiontek, PNY, all good distributors. DO NOT GET HERCULES! While great cards, they are confusing to use as they require their own set of drivers to run.
As for memory size--256 if you can. There's no reason not to if you have the cash. Just know how much you're willing to spend, and spend as much.
Ti4x00s are dated, MX4x0's are crappy, GF2 and 3's just don't size up, and the FX line is bad. Basically the entire nVidia line except the 6800 isn't worth the cash.
Final tips--Don't buy in a store. Buy it online, if you're American
www.newegg.com is a great store. Why? Is it slightly less secure? Not at all. Statistics are you're more liable to get robbed on the way to the store than to get your credit card number stolen, especially through such a trusted and known company as newegg. Seriously though, consider all these options, and choose your card carefully.
Also, don't forget about other games coming up. Half-Life 2, S.T.A.L.K.E.R., and more beyond the horizon.
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[This message has been edited by Dj Yoshi (edited July 13, 2004).]