The best commonly available low profile graphics card is the Radeon HD 7750 with DDR5 like
this one. In your price range Nvidia does not have any really good offerings, especially for low profile cards. The best low profile card Nvidia offers is the GT 640 found
here. The GT 640 is a good deal slower than the 7750. See the comparison
here.
Either card will run provided you have at least a 250 Watt power supply. If your power supply is weaker than that, you'll have to replace that too. The 7750 is an entry level gaming card, it will not max out Battlefield 3 at 1080p, but it will run games decently well at lower resolutions. If you feel you need more performance than that, you'll have to look at getting a new full sized case and a power supply to go with it.