i7 7700k is the minimum you want from 7th Gen. Many games utilize more than 4c / 4t and on top of that you want the extra breathing room to be able to record or play certain games without being pinned to 100%
If 8th Gen is too expensive, you should be building an R5 1600 / 1060 6GB build. Even the i5 8400 is miles ahead of the i5 7600k