With either CPU you can't get a high end GPU because the CPU would bottleneck it.
I say go with FX-6300 and get a decent CPU cooler at least Cooler Master Hyper 212 EVO. Once, you've done that start overclocking. With a decent mobo you should be able to hit around 4.7GHz.
I've overclocked FX-8120 to 4.4GHz and FX-6350 to 4.8GHz with
ASUS 970 M5A97 LE R2.0 and
Cooler Master Hyper 212 EVO. I say go with that mobo, it's good for overclocking and a solid mobo overall.
As far as not having a bottleneck stick with
R9 270X or
R9 280.
Overall FX-6300 is a decent budget CPU. Specially if you're running more things at once FX-6300 is a winner.