Should be more than enough, if that's some quality psu. Unless that's some cheap-ass unbranded model which only can deliver half its advertised output rating... (though, in fact, that should still be enough). Also, make sure the 12V rating is good enough, if that's an old 350W psu it might not deliver enough current on that rail.
Yeah, agree with previous poster that if it's a solid quality PSU, that SHOULD be enough for you methinks... If you take a pair of scissors to it and are able to cut it in half, then it won't do.
The PSU in my new box is 305W combined power and it drives up to at least a 3.6GHz prescott, 2 harddrives, 2 opticals and GF6800 vidcard (all standard components that can be had when ordering the system). So you should manage well enough I think provided you haven't bought some cheap-ass stuff that will float away if you fill it with helium.
2 of my friends had it and they weren't as lucky as I was. It litterally exploded in their cases.
My advice after my unfortunate accident with a much better psu?
Don't try to save money to such an important part of your system.
I agree, don't skimp on the PSU. Heck, Antec PSUs are quality, and you basically get a quality case for free.
I'm guessing a good 300W PSU should cover you, but double check to be sure. Even Antec seems to be moving to 350W as their new standard, tho, and that should allow for more upgrade headroom (for a 6800GT or 4000+).
My system killed a 431w Enermax with 20A on the 12V rail.
Went perfectly fine until i raised the ULTRA from 450 to 470mhz. That was just too much for the PSU. The OCZ Powerstream 520 is doing great with that clocks.
(Having tons of stuff like kathodes and crap hooked up on the PSU tho)