This is all generally for gaming. I'm deciding on these first before buying the rest of the parts for my first build. I know that I could probably upgrade the CPU more, but considering how this computer's main role will be for gaming, I have decided to spend more money on the GPU than the CPU. This combo costs about $360, more or less, and I can't really spend any more money on these parts...Will this be good enough for games such as Call of Duty Ghosts, BF4, etc.?
What he said, 270x is a good match for your CPU I would imagine. You wont be able to get an fx6300 due to your current fm2/fm2+ socket type though as far as I'm aware. I would still keep the CPU you mentioned, just because it is more current, and the AM3+ CPU's will be phased out sooner or later. It's always better to stay as current as possible when building a new PC IMO. However, it is entirely up to you.