I've recently upgraded from a 1070 to a 1080ti and I'm using a 4k screen. My best advice for you if you want to get the most out of your screen is to either wait until the next generation of Nvidia GPUs or get the 4k screen first and the 1080ti later when you have the budget .If you wait for the next generation, the 2070 or whatever it's called will most likely have a little more power than a 1080ti and cost half as much if you follow Nvidia's pattern.
Now speaking from my experience; setting everything to ultra except AA still isn't going to give you a solid 60fps on a 1080ti at 2160p. I've found that custom resolutions are the best here for being able to run ultra and still get a resolution close to 3840x2160(4k). For example a title that drops to 49fps on ultra at 4k, runs perfect at 3200x1800 or even 3456x1944. Those resolutions are pretty close to 4k (almost hard to for me to tell the difference especially with 3456x1944) at the same time perform great on a 1080ti and you can crank everything to ultra with the exception of AA which I would leave at the lowest setting(but not off).
If you go with the 1080, although it's not a bad card, you're probably going to regret not getting the 1080ti with that 4k screen. So I'd either get the 1080ti later on or wait for the next gen.
On a side note: Why not get a 6600k or 7600k? It performs the same (or better) as a 1700 at a much lower cost.