A few notes about building a gaming rig with the Pentium G4560 after a few trials;
1) any video card above 1050ti or RX 460 4GB will be bottlenecked by the CPU. A RX 470 or a GTX 1060 will perform better than the low-end cards, but would also lose around %10 of their performance compared to the same card paired with an i5. If it's the most bang for buck with a mid-end card you're looking for, this ain't it.
2) Don't go for any video card with less than 4G RAM. The newer games won't work smoothly.
3) The G4560 is the only CPU worth buying if you can't afford an i5. The i3 is utterly useless.