I recommend
1080P = 1060 3 GB => 1070
1440p = 1070 =? 1080 Ti
2160p = 2 x 1080 Ti
If ya budget doesn't allow for that at 1080p, then the RX570 .... once ya get to the 1060s level, AMD doesn't have a horse in the race.
Tho I wouldn't buy a 4k monitor until the new panels from AU Optronics drop which are 144 hz and HDR ready.
You can look here to see how the 1060 3 Gb / 6Gb and 1070 doe here in 18 popular games by hitting the next / forward buttons. The 2nd link gives ya 1070 / 1080 / 1080 Ti and has a bit more (22) games.
https://www.techpowerup.com/reviews/MSI/GTX_1060_Gaming_X_3_GB/22.html
https://www.techpowerup.com/reviews/MSI/GTX_1080_Ti_Gaming_X/25.html