Planning on buying GTX 760, will my FX 6300 bottleneck it?

Wondering if it will bottleneck during gaming,

NO

Nope, I have the FX 6300 and a 3GB EVGA GTX 580 and no bottle necks, it actually has preformed slightly better since I upgraded from an i7 860, not sure if the performance bump was from new build or just Windwos 8 over my old version of Vista.

Nope

You should be able to go all the way up to a 7970 or 770 without hitting a bottleneck.