I didn't want to compromise performance, but still wanted to somewhat keep with the red and black theme. Are you okay with the motherboard? It offers the best features for its price, but isn't in Red.
You can get the Gigabyte Z170X Gaming 3 which is red for 5 bucks more though.
The problem is I wanted to keep with your budget roughly put above, but putting the 850 Evo in pushed it to $1107. Hence why i've replaced it with the SP550, which is still a good SSD.
Cooler has been replaced with one that performs better, and is on sale at the moment.
Put it back in if you are willing to spend 30 bucks more, highly recommended.
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel Core i5-6600K 3.5GHz Quad-Core Processor ($219.99 @ Newegg)
Thermal Compound: Arctic Silver Arctic Alumina 5g Thermal Paste ($5.79 @ OutletPC)
Motherboard: Gigabyte GA-Z170X-UD3 ATX LGA1151 Motherboard ($129.76 @ OutletPC)
Memory: G.Skill Ripjaws V Series 16GB (2 x 8GB) DDR4-2800 Memory ($62.99 @ Newegg)
Storage: A-Data Premier SP550 240GB 2.5" Solid State Drive ($61.99 @ Amazon)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($47.49 @ OutletPC)
Video Card: Zotac GeForce GTX 1060 6GB AMP! Edition Video Card ($279.99 @ SuperBiiz)
Case: NZXT S340 (Black/Red) ATX Mid Tower Case ($64.99 @ SuperBiiz)
Power Supply: SeaSonic S12II 620W 80+ Bronze Certified ATX Power Supply ($62.99 @ SuperBiiz)
Operating System: Microsoft Windows 10 Home OEM 64-bit ($88.89 @ OutletPC)
Wireless Network Adapter: TP-Link Archer T4U USB 3.0 802.11a/b/g/n/ac Wi-Fi Adapter ($29.95 @ Amazon)
Other: Be Quiet! Pure Rock CPU Cooler ($24.90)
Total: $1079.72
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-08-19 22:54 EDT-0400