As
@Void said, APU is more of a choice if you're low on budget, since it combines both a CPU and a GPU. If you can afford spending more, I suggest you to go with a CPU + separated GPU. Otherwise, if you can't, and I think considering you're mentioning a PC build, you're speaking about a desktop PC, you could still go for an AMD A10-7670K or A8-7670K. They're quite decent considering the price (Graphics are R7, ok, it's starting to get a bit old, especially with the next Polaris GPUs, but better than nothing, and the CPU is a Quad-Core around 3 or 3.2GHz, which is enough to run most of today's games. Last time I checked the price (in Euro, since I'm in France), it was around €130 (~$150/160)).
Conclusion: Go for it if you absolutely need your computer as soon as possible without cashing too much, or wait to get a better processor, and a better graphic card (Plus, the Polaris GPUs AMD shown at E3 during the PC Gaming Show will be out soon, and apparently, they won't be that expensive (around €150-200 if I recall what I read on the French internets)).