1. Ryzen does many things well but gaming isn't one of them. I'll give ya the data and yu can decide for yaself
Anadtech CPU Bench comparison
Game / Ryzen 1600 / 7600k
(1080p) GTX 1080: Civilization 6 / 60.43 / 49.40
(1080p) GTX 1080: Ashes Escalation / 66.50 / 57.74
(1080p) GTX 1080: Shadow of Mordor / 136.18 / 146.64
(1080p) GTX 1080: RoTR-1-Valley / 93.54 / 141.33
(1080p) GTX 1080: RoTR-2-Prophets / 89.42 / 112.71
(1080p) GTX 1080: RoTR-3-Mountain / 115.59 / 145.21
(1080p) GTX 1080: Rocket League / 119.76 / 184.87
(1080p) GTX 1080: Grand Theft Auto V / 84.97 / 88.59
That's a total of 766.39 fps for Ryzen 1600 and 926.49 fps for the 7600k, a 21% advantage to Intel.
Wehen w elook at TPus testing ...
BF1 / 173.80 / 222.10
Civilization VI / 79.50 / 57.30
DeusEx Mankind Divided / 96.60 / 123.60
Dishonored 2 / 86.90 / 97.50
Doom / 195.40 / 197.60
Fallout 4 / 62.30 / 82.50
Far Cry Primal / 95.80 / 128.00
Hitman / 79.90 / 95.70
Resident Evil 7 / 269.30 / 273.20
RotR / 122.70 / 204.00
Sniper Elite 4 / 151.30 / 182.60
Styx: Shards of Darkness / 210.30 / 233.60
Total War: Warhammer / 68.10 / 87.80
Watch Dogs 2 / 101.70 / 86.70
Witcher 3 / 129.00 / 139.30
That's a total of 1922.60 fps for Ryzen 1600 and a 2211.50 for the Intel 7600k ...a 15% advantage.
Ryzen 1200 - "Gaming performance doesn't match up to competing Intel parts"
https://www.techpowerup.com/reviews/AMD/Ryzen_3_1200/21.html
Ryzen 1300X - "Single-threaded performance still lags behind competing Intel chips; Gaming performance slightly behind Intel chips"
https://www.techpowerup.com/reviews/AMD/Ryzen_3_1300X/21.html
Ryzen 1400 - "Gaming performance in the league of cheaper Core i3 dual-core parts"
https://www.techpowerup.com/reviews/AMD/Ryzen_5_1400/21.html
Ryzon 1500x - "Gaming frame-rates lower than competing Intel chips"
https://www.techpowerup.com/reviews/AMD/Ryzen_5_1500X/20.html
Ryzen 1600 - "Gaming frame rates lower than competing Intel chips"
https://www.techpowerup.com/reviews/AMD/Ryzen_5_1600/21.html
Ryzen 1600x - "Gaming frame rates lower than competing Intel chips"
https://www.techpowerup.com/reviews/AMD/Ryzen_5_1600X/20.html
Ryzen 1800x - "Limited game performance"
https://www.techpowerup.com/reviews/AMD/Ryzen_7_1800X/16.html
And there are other common issues listed in each review for a gaming box such as ...
-No IGP for that 2nd monitor to list system temps/ voltages, Discord, gaming web sites, etc
-Fewer memory options
-Complicated memory setup
-Little OC Headroom
Here we see the $205 7500 outperforming the $215 1600 and $240 1600x. That $35 cost performance pays for one of the best coolers on the market (Scyther Mugen Max)
An argument can be made that Ryzen gets cheaper because the MoBos are cheaper ... but that's an "apples and water melons" comparison. Yes you can use cheap MoBos, even on both ppoatforms with Intel B / H series. But the question is ... will the serve your needs. With Intel, you may have toi look harder for the bargains.
MSI Z270 SLI is $102 and w/ Intel CPU it gives you ..
-2nd Monitor option on IGP
-Option to upgrade to overclocklable CPU if ya don't get one outright (I would)
-2nd GFX card option
-up to 3800 memory speed
-2 M.2
-top level ALC 1220 audio
-Intel I219-V LAN
-6 fan connectors
For about $86 i can get the Gigabyte GA-AX370-Gaming w/ 20% off and $10 rebate as above ... for $16 is it worth losing ...
-No Monitor option on IGP
-No 2nd GFX card option
-600 drop in memory speed (I wouldn't miss this)
-only 1 M.2
-ALC 1220 audio drops to last generation extreme low budget ALC 892
-No more Intel LAN
-? fan connectors
2. Here's how the 580 and 1060 compare according to techpowerup
At 1080p the AIB 580 is about 3% faster than the reference 1060 and it overclovks 4.4% above that.
At 1080p the AIB 1060 is about 3% faster than the reference 1060 and it overclocks 15.1% above that.
So the 580 and 1060 are basically on an even keel... except if ya useing MSI Afterburner, you can expect about a 10% advantage from overclocking
3. 2 x 8 GB is the way to go go RAM, given current pricing DDr4-300 is only a few bucks more than 2133, so go for it.
4. Storage ... If ya get an SSD, don't get less than 250 GB. Id SSD kills ya budget, get an SSHD and out off the SSD for an upgrade. The SSHD will be 50$ faster than any HD ya can buy.