I also agree with refillable; and that you don't need a 600W PSU for a HD6770 or even a HD6870.
With a $300 budget, I'd probably do something like this:
Acer S200HLAbd Black 20" 5ms LED Backlight Widescreen LCD Monitor
Model #:ET.DS0HP.A01
Item #:N82E16824009317
$139.99 -$40.00 Instant $99.99
This monitor is 1600x900. I recently got the 1920x1080 version of this monitor (with the LED backlighting) and I really like how nice it looks. I think the $10 over a non-LED version is worthwhile. I didn't go for the full 1080p to keep GPU requirements consistent with your budget.
Antec EarthWatts EA-500D Green 500W ATX12V v2.3 / EPS12V 80 PLUS BRONZE Certified Active PFC Power Supply
Model #:EA-500D Green
Item #:N82E16817371035
Mail in Rebate
$89.99 -$32.00 Instant $57.99
There's a rebate on this too. The Earthwatts PSUs are very solid, and also quiet. This is a good deal on the $500W version.
HIS IceQ X Turbo H679QNT1G2M Radeon HD 6790 1GB 256-bit GDDR5 PCI Express 2.1 x16 HDCP Ready CrossFireX Support Video Card ...
Model #:H679QNT1G2M
Item #:N82E16814161371
Mail in Rebate Card
$149.99 -$10.00 Instant $139.99
The HD6790 has a 256bit memory path, so it is actually a visible step up from the 128bit HD6770. There's a rebate on this one too, if you play that game (and win).
Subtotal: 297.97
If you can stretch your budget another $10, you can get a HD6850; there's a HD6870 at that price too, but I wouldn't get that one. Although I normally like HIS, the comments seemed to indicate possible quality issues.
Edit: There were a couple of cheaper options iirc, but the ones I chose also had free shipping.
If you have no desire to replace your monitor (seriously, you'll wonder why you didn't when you finally do), then a HD6670 is likely all you need, and as stuffe said, doesn't need auxiliary power. Any good 300W PSU can run it.
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