I may not have gotten the BEST deal here, but I think this is probably along the lines of what you might want.
The bitfenix prodigy can't run 2 graphics cards due to mitx motherboard.
i5 4570, a good cpu, decent heat with stock cooler which won't cause the rest of the build to get too hot in mitx case.
GTX 750ti will run med/high settings in Battlefield with a good solid framerate. You can upgrade this later.
1x8gb Corsair Vengeance 1600mhz low profile ram, with only 2 RAM slots this means you can upgrade to 16gb later if you feel the need.
OS included, no other peripherals tho and no optical drive, you could add a standard optical drive tho and still stay around budget.