The AMD RX 480 should perform way better than the 960, kind of like 970 or even better.
Also instead of buying that expensive case fan, get Cooler Master Sickleflow for way less money -
http://ca.pcpartpicker.com/product/wL3RsY/cooler-master-case-fan-r4l2r20arr1
A cpu cooler is not needed. The I3 6100 comes with a stock cooler which is perfectly capable of cooling it under full load. Put the money elsewhere, like more ram, or better motherboard.
So final build -
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel Core i3-6100 3.7GHz Dual-Core Processor ($147.98 @ DirectCanada)
Motherboard: Gigabyte GA-H110M-A Micro ATX LGA1151 Motherboard ($38.98 @ Newegg Canada)
Memory: Kingston HyperX Fury Black 8GB (1 x 8GB) DDR4-2133 Memory ($35.99 @ Amazon Canada)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($60.43 @ Vuugo)
Case: NZXT Source 210 (White) ATX Mid Tower Case ($44.88 @ Canada Computers)
Power Supply: EVGA SuperNOVA GS 550W 80+ Gold Certified Fully-Modular ATX Power Supply ($89.98 @ Newegg Canada)
Optical Drive: Lite-On iHAS124-14 DVD/CD Writer ($14.99 @ Amazon Canada)
Operating System: Microsoft Windows 10 Home OEM 64-bit ($117.98 @ DirectCanada)
Case Fan: Cooler Master SickleFlow 69.7 CFM 120mm Fan ($6.66 @ DirectCanada)
Case Fan: Cooler Master SickleFlow 69.7 CFM 120mm Fan ($6.66 @ DirectCanada)
Other: AMD RX 480 8GB ($280.00)
Total: $844.53
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-06-25 18:20 EDT-0400
Changed the RX 480 to 8GB version. Wait for it to come to market, should be available from first week of next month (july). Note it is estimated price. Price should not vary that much from this estimation.