This should work very well with the Rx 480:
PCPartPicker part list:
http://pcpartpicker.com/list/X9P8NG
Price breakdown by merchant: http://pcpartpicker.com/list/X9P8NG/by_merchant/
CPU: Intel Core i5-6500 3.2GHz Quad-Core Processor ($204.99 @ Newegg)
Motherboard: Gigabyte GA-H170-GAMING 3 ATX LGA1151 Motherboard ($104.99 @ Newegg)
Memory: G.Skill Ripjaws V Series 16GB (2 x 8GB) DDR4-2400 Memory ($66.99 @ Newegg)
Total: $366.97
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-07-25 14:16 EDT-0400