Personally I would NOT go for a 6800 with an nforce3 motherboard. Whereas you will probably be able to run it OK, it won't overclock much (I don't know why, but there seems to be some kind of incompatibility between (nvidia's!) 6800 and (nvidia's!) nforce3 chipsets. They just don't overclock well together.
This - combined with the additional annoyance of the borked 6800 video processor - tips the scales in favour of an X800, imho. Personally I would go for an X800 XT or an X800 Pro vivo and unlock all 16 pipes.
I say this as an nVidia GF6800GT owner. Overall I am happy-ish with the card but in hindsight I would get an X800.
(Strangely the GF6800 overclocking problem does not exist with Athlon XP systems. I don't know why. I could clock my card up to 453MHz on my old DFI Ultra Infinity. 445MHz was completely stable and artefact free. Now in my K8N, it won't do more than 415 without lockups. I am lucky, many won't do 400! And before anyone jumps in with "disable fastwrites", that is NOT the problem. It fixes it for some people struggling with minimal overclocks, but it does nothing for me. Neither does setting 2d and 3d clocks the same, nor playing with other AGP settings. I am stuck with it they way it is.)
Chip
EDIT: sorry, just saw your budget. Obviously the cards I mention are too expenive. Still, don't get an 6800.