The best GPU would probly be an HD7750 as they don't require extra PCIE power and make very little heat.
HIS iCooler H775F1GD Radeon HD 7750 1GB on New Egg for $110. About double the performance of a 6670 GDDR3, super quiet and Windows rates it at 7.4/7.4 on the Windows Experience rating...(yeah its not the best benchmark I know)
I'm going to go ahead and suggest that you upgrade your PSU regardless - I'd imagine the thing still has the original supply, which would be junk. This is an affordable, high-quality PSU that can easily handle what you'll be working with.
I have installed many sapphire HD5000 and HD6000 series GPU's and never had a problem that wasn't the users fault (bad flashing). I would suggest HIS but not with this cooler design, so go with the Sapphire you wont be disappointed, it should be almost double the performance of the 6670 and still be very quiet and cool.
Hey guys, I went with the SAPPHIRE Radeon HD 7750, and it was piece of cake installing it (had to rip out some random flimsy metal junk by the slot, but that was no big deal). It fits perfectly, and it is a pretty sweet card. Best I've ever had, as I tend not to splurge on components, and I also have a company to run from the same comp, so a really sweet graphics card would be rather distracting.
I tested an old WOW account, and maxed out the settings and got 60fps...better than the 24 I was getting on "Good" settings.
For those of you not using Dropbox, I want to score some free space. It is an awesome program, and great with an iPhone. Shameless plug, I know, but I love free storage space;) http://db.tt/dlyr8Ke