The R7 240, 250 and 260 cards seem to be the best fit for your system, go ahead and look them over and pick the one that fits your rice range best, the 240 and 250 do not need extra power, the 260 does, but all should work with a 350w PS you have. Your MB looks like PCIe 1.0 x16, all of the cards here are 3.0 but that should be fine.
The 240 are around $70. None of these are really strong for gaming, but the 260 will game the best at that price. hope this helps..
A quick google revealed this price per game performance benchmark updated every 24hrs http://www.videocardbenchmark.net/gpu_value.html Hope it helps.Also I would check the top few on the list in shopping search engines to see if there is a better deal.