Do you have a gsync monitor? That would be the only reason to require a 1060 or 1050ti. The Rx 580's prices have come down and they are even when it comes to performance with a 1060 6gb. I would go with a 580 which is significantly faster than the 1050ti.
PCPartPicker part list:
https://ca.pcpartpicker.com/list/h4cVZR
Price breakdown by merchant: https://ca.pcpartpicker.com/list/h4cVZR/by_merchant/
CPU: AMD - Ryzen 5 2600 3.4GHz 6-Core Processor ($222.41 @ Amazon Canada)
Motherboard: ASRock - B450 Pro4 ATX AM4 Motherboard ($95.50 @ Vuugo)
Memory: G.Skill - Aegis 16GB (2 x 8GB) DDR4-3000 Memory ($149.99 @ Newegg Canada)
Storage: Crucial - MX500 250GB 2.5" Solid State Drive ($68.00 @ Amazon Canada)
Video Card: MSI - Radeon RX 580 8GB ARMOR OC Video Card ($299.99 @ Newegg Canada)
Case: Phanteks - ECLIPSE P400 TEMPERED GLASS ATX Mid Tower Case ($99.99 @ Memory Express)
Power Supply: SeaSonic - S12II 520W 80+ Bronze Certified ATX Power Supply ($64.99 @ Newegg Canada)
Total: $1000.87
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-10-29 15:30 EDT-0400
Here is a 1060 build with a cheaper mobo and PSU.
PCPartPicker part list:
https://ca.pcpartpicker.com/list/M7tHbX
Price breakdown by merchant: https://ca.pcpartpicker.com/list/M7tHbX/by_merchant/
CPU: AMD - Ryzen 5 2600 3.4GHz 6-Core Processor ($222.41 @ Amazon Canada)
Motherboard: ASRock - B450M-HDV Micro ATX AM4 Motherboard ($65.50 @ Vuugo)
Memory: G.Skill - Aegis 16GB (2 x 8GB) DDR4-3000 Memory ($149.99 @ Newegg Canada)
Storage: Crucial - MX500 250GB 2.5" Solid State Drive ($68.00 @ Amazon Canada)
Video Card: EVGA - GeForce GTX 1060 6GB 6GB GAMING Video Card ($337.99 @ Amazon Canada)
Case: Phanteks - ECLIPSE P400 TEMPERED GLASS ATX Mid Tower Case ($99.99 @ Memory Express)
Power Supply: Corsair - CX (2017) 450W 80+ Bronze Certified ATX Power Supply ($49.99 @ Corsair)
Total: $993.87
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-10-29 15:34 EDT-0400