The FM2+ Processors are the best choice for your situation. Not only do you get a decent CPU or APU, With paired with an Integrated or Discrete GPU, You can play at 1080p fairly well. Sure, APU's are not the best option for gaming, but if you are on a tight budget (Say, $500), It makes good sense to go with a Processor from the FM2+ Socket.
The Best CPU in the FM2+ socket for the money is the Athlon X4 860K. At $85, You are getting an Awesome Quad-Core CPU clocked at 3.7 Ghz, a Decent 4MB L2 Cache, and the ability to Overclock it. Pair it up with a GPU, however, since it does not have integrated graphics. However, the R7 260X or R9 270X will be perfect when combined with the Athlon, as it will allow you to game at 1080p with no issues.
The Best APU? I'd Argue the A10-7850K. Sure, the $175 price tag is quite ludicrous, But for it you get the same stats as the Athlon X4 860K, Except they add in Integrated Radeon R7 Graphics. It's not the best option for gaming, but if you put it up with AMD Radeon R9 RAM at 2400 Mhz. (Yes, AMD Also makes RAM as well), You can play some games at 1080p with little to no issues.
Overall, The APU's and Athlon's are extremely underrated. They do decent gaming at a reasonable price. Plus, They are one of the best options out there if you want to game on a Budget.