At the right price, a 7th gen processor system could still be a reasonable choice. However, it is worth pointing out that the i3-7350K is only a 2 core, 4 thread processor, which could hamper performance in some newer and upcoming titles. The i3-8350K lacks hyperthreading, but has 4 cores, which should give it better performance in games where all cores are being fully utilized. The Coffee Lake CPUs are in short supply at the moment though, and might continue to be hard to find for some weeks, or maybe even months.
Going with an i5 might also be an option worth considering. The new i5-8400 is not unlocked for overclocking, but has 6 cores, and should offer a bit better performance in most games than an overclocked Ryzen 1600, at a similar or lower price. It does lack hyperthreading though, so the Ryzen can still outperform it in heavily multithreaded applications, but that doesn't apply to most games, where its 6 cores should be plenty for some time. You do still need to pay more for a z370 motherboard though, at least until Intel launches their lower-end motherboard chipsets, but that won't likely be for a few months. You might need to wait a bit if you go the Coffee Lake route.
Aside from that, ideally, you'll want at least 8GB of RAM for a gaming system. 4GB should work for most games, though you may run into occasional performance issues. Unfortunately, the cost of RAM has gone way up over the last year due to a shortage, and it will probably be some time before the price comes back down. And as for the video card, a 1060 6GB will perform a lot faster than a 1050 Ti. Performance in games can be over 50% faster in cases where your CPU isn't holding it back. Just another thing worth considering.