First off, Unless you have a quality brand power supply like Seasonic or Corsair, That is either 80 Plus certified or higher in its efficiency rating, I wouldn't recommend any card that pulls anthing more than the power from an AGP or a PCI Express slot becasue it might not even be putting out a clean and stable 350 watts. What processor are you running? What are your other system specifications?
I can tell you now, With a 350 watt power supply, you won't be running a high end card, and even if the card could technically play BF3 or BF4, It will play it at such a low resolution and detail with such low frame rates that the game will be unplayable.