The gtx 1060 and amd 480 will be ideal for 1080p 60hz screen, where the gtx 1070 will be overkill for that type of screen. I currently have a gtx 1070 for a 1080p 60hz screen, framerates kill my screen, so vertical sync is almost a must, so I need to consider a 144hz screen.
Personally, I'd go for the gtx 1070, a little more future proof, where I don't care right now I've outclassed my monitor, I love that I can run any game no problem at 1080p. The gtx 1070 is probably a true 1440p card, but defiantly not 4k.