Using a few different PSU calculators, I get between 600-800W usage under full load with your cpu overclocked and 1070 boosting a decent amount. You can get by on a 650, 800, or 1000W PSU for sure, but quietly is a different story. Most quality PSU's can provide slightly more power than they are rated for, so you likely wouldn't see shutdowns on a 650 or 800W PSU, but that is not what I would recommend, especially if you plan to keep the unit for a long time and use in any future builds.
Look for a PSU that is silent or has an "eco mode" such as EVGA's platinum and titanium units, as well as corsairs AXi or HXi series. These units provide very good power, and the high end models are silent up until around 500W, or a specific temp to be exact, when the fan kicks in to around 1000 rpm. Pretty much every PSU on the market has a good review on it that includes metrics such as noise and temperature. They will tell you how the PSU in question will operate at a given load range. Having said that, I cannot find very good data indicating the Seasonic 850 Prime Gold will be as quiet as you want. It has a hybrid mode, but none of the reviews give a graph of load vs fan rpm, and fan rpm vs noise, so its hard to say if that psu will be as silent as you want. A higher efficiency psu will do better on this front
I am in the process of replacing my old EVGA 1300G2 right now for a 1600T2, since my G2 is becoming very (relatively) loud since I am watercooled. I hear it 24/7 over my case fans, and wanted to upgrade to something that is silent at idle and small loads. I believe it is worth the investment. You will hear your 1070's over most PSU's under a loads, so the decision to go bigger isn't as critical. When you start to watercool everything, all you have to hear is your rad fans and the psu, the so decision to get a high end PSU become's more critical.
5760x1080 120hz Lightboost gaming FTW!!!!!!!!!!