With the Ryzen 2000 series CPUs, it really makes it difficult to suggest an Intel CPU given the pricing. The excess cost of a Intel CPU does not justify the 5% fps increase. If you want to stream, then AMD CPUs make even more sense as streaming runs best with more threads and AMD CPUs biggest benefit is the amount of threads provided for the cost of a CPU.
I would go with a 2600 as it is a 6 core 12 thread CPU that can do a lot of different things. Some of the games you listed are not demanding, while others are demanding. If you want 80-90fps in demanding games, you will need a better GPU than a 1060/580. I would look at a 1070 or higher.
The 1070ti is a good price and is very close to a 1080 and it seems to be the best for price vs performance in that GPU tier.
I would go with something like this, it will be a very good gaming rig for several years and has a good foundation that can be upgraded as new parts come out.
PCPartPicker part list:
https://pcpartpicker.com/list/VtJgq4
Price breakdown by merchant: https://pcpartpicker.com/list/VtJgq4/by_merchant/
CPU: AMD - Ryzen 5 2600 3.4GHz 6-Core Processor ($165.99 @ Amazon)
Motherboard: MSI - B450 TOMAHAWK ATX AM4 Motherboard ($89.89 @ OutletPC)
Memory: G.Skill - Ripjaws V Series 16GB (2 x 8GB) DDR4-3200 Memory ($134.99 @ Newegg)
Storage: Crucial - MX500 500GB 2.5" Solid State Drive ($89.85 @ OutletPC)
Video Card: EVGA - GeForce GTX 1070 Ti 8GB SC GAMING ACX 3.0 Black Edition Video Card ($389.99 @ Newegg)
Case: Fractal Design - Focus G ATX Mid Tower Case ($51.15 @ Amazon)
Power Supply: EVGA - SuperNOVA G2 550W 80+ Gold Certified Fully-Modular ATX Power Supply ($57.99 @ Newegg)
Total: $979.85
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-10-02 09:50 EDT-0400