Almost all current cards are past shader model 3.0(that was Direct X 9c). You will see all kinds of DirectX11(shader model 5) card kicking around.
The 7750 listed above should work. Again, this all relies on the system delivering the labeled wattage.
AMD's official recommendation is a 400 watt power supply. But it all depends on the rest of the system.
Please also check to see if your case requires a lot profile card or not.
A 5570 is another card that would work, but IMO it is just too slow and takes almost as much power.
You can look here for some benchmarks and power use for the card(both the 5570 and 7750 are listed) it self(not including the system).
http://www.techpowerup.com/reviews/HIS/HD_7750_iCooler/24.html
This is all 100% based on the power supply delivering what it says it can. and a 65 watt cpu(if you give me the model number of the cpu I can check that).