That budget pretty much rules out any good 4k monitors. Most good quality 4k monitors are in the 400+ range(usd).
1440, imo, is a better option. Less demand on the gpu and still an awesome quality picture. My current monitor was on the upper end of your budget, but very worth it imo. Dell s2719dgf. 27in, 155hz. 1ms response time. Its priced currently at about 400us, but I'm sure with some black friday sales will dip into the low 300 range. It goes on sale regularly. I snagged mine for 330 from bestbuy.
That being said, if this is a gaming rig. That 1060 is going to struggle at either of those resolutions. 4k is almost out of the question unless you want to play in the under 25fps. Even at 1440p alot of titles will struggle to reach much more than 60, if they even hit 60.