If it were my rig, I would not go with the 1600. AMD's Ryzen CPUs are really good, but the 1600 is a generation old and Intel's 8400 clearly beats it in performance. The 2600 is a good option, but it will cost a little bit more because you will want faster RAM and x470 motherboard for plug and play.
I would also drop to 8gb of RAM for now. 8gb is plenty for today and if you need more you can upgrade down the line. Any RAM not used by an application will just sit idle. RAM prices are crazy high, so it may be cheaper to upgrade in a year or so. 18 months ago you could get 16gb of RAM for around $80. Today it is twice that much.
I would also go with the 6gb version of the 1060 over the 3gb as there is a big difference in performance. Additionally, the RX 580 has very similar performance as the 1060 and you will be able to use free sync. So I changed your monitor to a free sync monitor. This will also butter smooth gameplay and is a really nice piece to a gaming rig.
I also swapped out the PSU for a little better quality unit.
PCPartPicker part list:
https://pcpartpicker.com/list/st4bpG
Price breakdown by merchant: https://pcpartpicker.com/list/st4bpG/by_merchant/
CPU: Intel - Core i5-8400 2.8GHz 6-Core Processor ($178.99 @ Amazon)
Motherboard: Gigabyte - B360M DS3H Micro ATX LGA1151 Motherboard ($68.09 @ Amazon)
Memory: Patriot - Signature Line 8GB (2 x 4GB) DDR4-2666 Memory ($78.99 @ Amazon)
Storage: Crucial - MX500 250GB 2.5" Solid State Drive ($69.89 @ OutletPC)
Storage: Western Digital - Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($43.90 @ OutletPC)
Video Card: PowerColor - Radeon RX 580 8GB Red Devil Video Card ($269.99 @ Amazon)
Case: Phanteks - ECLIPSE P400 TEMPERED GLASS ATX Mid Tower Case ($79.99 @ Amazon)
Power Supply: Corsair - CX (2017) 550W 80+ Bronze Certified ATX Power Supply ($29.99 @ Newegg)
Monitor: Acer - ED242QR Abidpx 23.6" 1920x1080 144Hz Monitor ($189.90 @ Amazon)
Total: $1009.73
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-06-27 13:05 EDT-0400