Ah i already answered your additional question, but I put it again.
i5 will get more fps, they always do, but not at hurting level.
https://www.youtube.com/watch?v=8ugae-4ja5o
i copied and paste it again here, this is a decision that decide your 4 year pc build.
AMD has 6 core 12 thread (some lucky guy get 8 core 16 threads), intel i5 8400 has 6 core 6 thread. Does thread useful? well the answer a bit long and my "over simplified" answer might enraged some expert but I explain it in my own way anyway. 2016 is the start of the game revolution as the game maker were "forced" to use more than 4 thread (yeah, before 2016, games were only optimized for 4 thread). The normal common term is "i5 killer" since at that time i5 only have 4 core. Then again until Q1 2018, I only see 6 thread or less optimized game, above 6 thread is very rarely seen. Now the question is, will you risking your build with i5 that only has 6 thread? For me, its safer go with Ryzen 5 1600 or go directly to i7. $100 upgrade to i7 will put you in longer safe. Why? look at those owner of i7 before 2016, they have no problem since they have 8 thread.
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel - Core i7-8700 3.2GHz 6-Core Processor ($299.00 @ Amazon)
Motherboard: Gigabyte - B360M DS3H Micro ATX LGA1151 Motherboard ($67.57 @ Amazon)
Memory: Team - Dark 16GB (2 x 8GB) DDR4-3000 Memory ($159.89 @ OutletPC)
Storage: Patriot - Ignite 480GB 2.5" Solid State Drive ($99.89 @ OutletPC)
Video Card: EVGA - GeForce GTX 1060 6GB 6GB GAMING Video Card ($294.88 @ OutletPC)
Case: Thermaltake - Versa H21 Window ATX Mid Tower Case ($19.99 @ Newegg)
Power Supply: SeaSonic - S12II 620W 80+ Bronze Certified ATX Power Supply ($48.89 @ OutletPC)
Total: $990.11
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-04-24 22:54 EDT-0400
Its $90 over your budget, but its a long term safe net. You will have no worries about AMD inefficiency, and free from future "i5 6 thread killer"