A budget no name 680 watt PSU wouldn't be much good, and neither would a 700watt budget PSU. There are certain companies that are really good PSU vendors: Antec, Enermax, Seasonic, Thermaltake, Corsair etc.
Here's a good site for PSU reviews and information:
A budget PSU from a no name company like Raidmax might work, but it has cheaper components and experiences a higher failure rate. I try to read reviews of PSU's that I buy, and the last time I bought a barebones system, I switched out the Raidmax PSU for an Antec True Power.
Overall, the financial way of determining if you have a good PSU is to spend at least $79, the old fashioned heft way is to hold it in your hand and note how heavy it is compared to a similar wattage no name brand.
You need to make sure you have enough amps on the 12 volt rail for your card. Check at AMD/ATI for recommended PSU's and check under each card's specs for how many amps it needs. Here's the page:
Overall, a 680 watt and a 700 watt are comparable. ATI's site lists some 550 watt PSU's that are certified with the 4850, so it depends on what else you have in your system. Make sure your case has enough cooling, because the 4850 doesn't vent the hot air out of the case.
Bad cooling can lead to the card overheating, as the case air gets too hot. If you have a budget case, you might want to save up and get the 4870 instead, but make sure the PSU is good to go, or swap it out for a better one.
Me, I love the Antec Nine Hundred, can't get better case cooling than that!