I'm making a very small PC, but I do need a good heatsink (no overclocking will be done)
NO LIQUID COOLING METHODS
Why the 7700k instead of the 8700k
Something like this:
should serve you very well. I am currently using a Cryorig cooler and it is very powerful and very quiet. You might also want to try something from be quiet! (the ! is part of the name I'm not just super hype about CPU coolers)
It should serve you well and be quiet in the process. I think either choice will be excellent. The main difference is that the Cryorig is 47mm and the be quiet! is 74.5mm. Both will fit in the case the be quiet! will be a bit tighter fit. The be quiet! is also about $20 USD more expensive than the Cryorig one.