This was my first time building a pc.
Why not a R5 1600, and have the extra 100 dollars go toward a 1080? More cores / threads, and better performance in games.
Because most games can't utilize more than 4 cores anyhow with the odd exception such as AOTS. Raw single core speed actually has more bearing on game performance than more cores. Several triple A titles are actually optimized for 4 cores because of the past several years of the i5 and i7 dominance for gaming and most others are more single core based such as most MMOs like World of Warcraft.
I am not saying Ryzen can't game, it can do so well but if you look at all the benchmarks online from gamers nexus, linus tech tips, jays2cents, pauls hardware etc the unlocked i5 and i7 cpus lead the top game FPS when overclocked due to pure core speed. Ryzen's advantage of more cores is useful if you do something that can use said cores such as video editing, live transcoding, virtual machines, etc.
I do see your argument on saving money on a CPU and going with a higher video card for FPS but there are a few factors we don't know. If OP is using a 1080p monitor then going from the 1070 to the 1080 will make zero difference. Also it depends on the games he plays too, if its games that are hard on GPUs then a better GPU and lower CPU won't be a big deal but if its a CPU demanding game then going with what he has is best.
However note to the original submitter of this build:
Great build overall, one upgrade I would suggest later on for quality of life using of the PC is a SSD. Even a cheap lower performing SSD is a night and day difference in using the PC compared to a mechanical drive (just won't increase game FPS).
Please keep feedback polite and constructive.