You kind of have the right idea, you want the CPU and videocard to be balanced. But for one thing, a 460 and a 470 are on two completely different performance levels. So you'd want to match the 460 to an entry level CPU, whereas the 470 works better with a mainstream CPU.
Your examples, the FX 6xxx series, are just fast enough to make the 470 the better choice.
I would not advise buying an FX CPU now, if you don't already have an FX system. If price is the issue, build a Pentium G4560 based system. It has more of a future upgrade path in the event you eventually want to upgrade your CPU. If AMD is your choice, the Ryzen 1400 is your current lowest price choice that makes sense.