So thread title mentions my current CPU a slightly OC'd 6600k. Considering the upgrade for gaming purposes as I notice the CPU as a potential bottleneck for some newer titles. My system is also running a gtx 1080 with 16gb of ram.
After a bit of research the aforementioned 2 processors in the thread title seem like they would be the best balance between significant boost in performance and budget. The caveat with the 8 series is having to get a new 300 series mobo. Currently a local retailer in my area has the 7700k on sale and is out of stock on the 8600k. It would save me the additional cost of a mobo upgrade but I'm considering the future proofing of an 8600k as well with the new mobo.
I believe you would be okay for a while, but later on you might want to consider upgrading to the 8th generation series. Both the 7700k and 8600k are more or less similar in performance for now https://www.techpowerup.com/reviews/Intel/Core_i5_8600K/18.html
but that extra two cores on the 8600k might come handy in the future as games gets more demanding, so it would be better to upgrade to the 8600k.