I agree with Cookybiscuit. I used to play Crysis 3 on a 6850 on a LGA 771 platform with a 3ghz xeon and was able to use high settings on a 1920x1200 monitor. If you are intent on keeping your current monitor, an AMD Radeon 260(normal or 260X) or Nvidia GTX 650ti boost would be all you need. The 760's and 270x at that resolution will run ultra on a 1080 solution.
Anand bench showing the 260X and 650 ti boost.http://www.anandtech.com/bench/product/1044?vs=1040
Your FPS will be significantly higher as you have roughly half the pixels/resolution to power.