@OP:
You can even play Dx11 games on a nVidia 8800GT or ATI 3870.....! Try to see things in perspective and do not get carried away with the big honcho company marketing. "Dx11". This API offers two critical things, Shader Model 5.0 and Tessellation. No suppose you would get a HD5750 -- touted DirectX 11 card. It will do things jack differently as compared to a high end GTX nvidia or HD48xx series. WHY..cause the card is just not powerful enough to render enough, to harness the full power of Dx11.
If you want to play full Dx11 then get a system like Ashu's -- and replace the GPU with a HD5850 or HD5870. (He is going to kill me for this).
Also resolution is really important to create a well balanced system within budgets. You mentioned you have a monitor. What resolution is it at..? Sam has mentioned a well balanced rig, but be rest assured, it will not give full eye-candy -- the Dx11 you want.