I'm going to assume you are running 1080p. A GTX 1060 (6GB variant) will be fine for that and save you a LOT of money over a 1070, especially if you get a factory overclocked one which can come within 10% of the performance of a standard 1070 (kind of like a 970 vs. a 980 from two years ago).
However, when you say "new games" don't expect even a 1070 to run the new Dues Ex at 60FPS at 1080p, because it won't unless you turn down quality and AA settings. Also, a lot depends on your CPU/motherboard which you don't reference. If you have a weaker chipset, that 1060 or 1070 can be bottlenecked.