if going with a 1080, I'd spring for the 8600K if possible, despite the extra $150 expense in cpu, cooler, mainboard...
The R5-1600, although quite competent, is not quite as fast as the 8600K, and lags on min framerates (in comparison with 8600K) on some games, especially if trying to maintain 144 Hz refresh rates. (If playing with 60 Hz refresh monitor, no perceived difference)
(The R7 variants are not faster than the R5-1600 in today's games, I'd only consider them if a heavy streamer and/or home video editor, etc...)