If the purpose of your PC is for PURELY gaming and nothing more, then, the Intel i7-7700K is your pick. However, as you mentioned, it costs way too much and its value has decreased with more affordable CPUs offering better price/performance ratios.
If the purpose of your PC is for gaming AND multi-tasking/editing/streaming, then, consider the AMD Ryzen 7 1700, instead of the above. However, like the i7-7700K, this CPU also costs a lot (though slightly less), so... consider the AMD Ryzen 5 1600 if budget is tight.
Still, if your budget won't fit with any of the above CPUs, consider the AMD Ryzen 5 1400 (the lowest-tiered/most-affordable CPU in the AMD Ryzen line up as of today). Getting this CPU will allow you to upgrade to any of the AMD Ryzen CPUs mentioned above (which costs less than their Intel counterparts).
Further still, if your budget won't fit with any of the above CPUs, including the most affordable CPU in the AMD Ryzen line up, then, you have to pick the very very affordable Intel Pentium G4560. Getting this CPU will allow you to only spend less - but, it will limit your options in the future when you decide to upgrade the CPU to only Intel i5's or i7's, which are more expensive than AMD Ryzen 5's and 7's.