I got 2 GTX1070's (Haven't updated my sig) and I play at 1440p, and I tell ya they are overkill for most games, Though 1080p at high refresh rate you may want to get a 1070 or 1080 if you can afford it.
At 1080p 60hz, a gtx1060 will be more than enough, though I do recommend that you get the 6gb 1060. The 3GB 1060 is slightly slower, and at 1080p there are more and more games that will need more than 3gb.