I have the fx6300 at stock speeds paired with a gigabyte g1 gaming 1060 3gb OC and it works very well. The only slowdowns you get in games are due to the processor not the gpu and games run at ultra 55fps+ 1080p but here is some more information since i spent a long time researching this.
Nividia GTX cards
1050 - not a great card
1050Ti - slightly underpowered
1060 - Price to performance sweet spot will work well with a fx6300
1070 - will not reach its full potential in basically every game so not worth the extra cost
1080 - heavy bottlenecks should be no differance in fps from 1070
1080 TI - if you can afford this card you can afford an I7 6700k so why ask.
AMD RX cards.
460 + 470 - low end cards not recomended
480 - perfect card for...