I think the AMD A10-6800K Richland 4.1GHz (4.4GHz Turbo) Quad-Core Desktop Processor - Black Edition with integrated AMD Radeon HD 8670D video is a good affordable CPU for gaming since it cost $140 on Newegg, and it has has integrated AMD Radeon HD 8670D which is pretty good for playing many PC games on medium to high video settings without the need to buy an additional PCI-Express video card like the Nvidia GTX 660 2GB.
Ya that seems to be a good option but make sure you see its review videos on youtube.com first. I think integrated graphics are a bit slow atm for gaming performance though they are good for decent computing needs.
I read posts on blogs that some Integrated graphics from AMD CPU with Radeon HD 8670D and Intel HD 5000 built-into newer Intel CPU can be good enough for Minecraft, League of Legends, Dota 2, and other games.
But, games like Crysis 3, and Battlefield 4 are better with a dedicated video card like the Nvidia GTX 660 card if you want to play games at higher graphics settings on a high resolution 1080P monitor.
I highly recommend you go with an Intel processor, it is worth the slightly higher price tag for what you get. The performance is great and the built in graphics are fine for mid-level gaming.