You will get better performance from an i3 6100+GTX 1060 3GB in games. I'd recommend the i3 7100 over the i3 6100 as its only about $7 more, and the 4GB RX 480 over the GTX 1060 3GB.
If you are planning to maybe upgrade your processor again in the future to a nice i5 7600k or i7 7700k to take advantage of your very nice motherboard, i would recommend this.PCPartPicker part list
/ Price breakdown by merchantCPU: Intel Pentium G4560 3.5GHz Dual-Core Processor
($59.63 @ OutletPC) Video Card: Zotac GeForce GTX 1060 6GB 6GB AMP! Edition Video Card
($239.99 @ Amazon) Total:
$299.62Prices include shipping, taxes, and discounts when availableGenerated by PCPartPicker 2017-04-15 18:39 EDT-0400
The G4560 is a little beast of a processor for its price, being barely weaker than the i3 6100 at a much lower price. This reduce in cost would allow you to buy a GTX 1060 6GB. I would rank the cards like such: 1060 3GB> RX 480 4GB> RX 480 8GB/GTX 1060 6GB.