1600x1200 - ah 4x3, we knew you well.
That's about 7% less pixels than a 1080p monitor. Ok, Blizzard games aren't very GPU demanding compared to some others. That said, there's a big step in gpu needed between running at high quality and ultra/extreme. Here's a couple of benchmarks for Wings of Liberty:
Tom's Hardware @ 1080p, High Quality (probably using 4x AA) in DX11
Anandtech Bench @ 1920 x 1200, Ultra Quality and 4x MSAA in DX9. This is the worst of the worst cases. DX11 will bump fps by 10 or more. MSAA is a resource hog. 1920 x 1200 is 20% more pixels to push.
Notebookcheck benchmarked HotS, showing a tad less fps than WoL.
That said, the low end is probably the HD7750. Figure your fps will be in the 30-40fps range maxed out, or above 60 with some bells/whistles turned down. You can still go
passive with this card. If it has a thermal issue in your case, it's easy to just zip tie a 500rpm silent 120mm case fan onto it and call it a day.
The next step up is fanned, and there's the HD 7770 and the new HD 7790. On the NVidia side, there's the GTX 650 and the GTX 650 Ti Boost. Go for the 2GB versions as games are starting to creep up in the amount of RAM they are using. Asus and MSI seem to have the quietest versions out there. Once you settle on the class of card, we can drill down into which one is the best for you.