Liquid cooling, even all in one closed loops, usually has a few more steps than a traditional air cooler. Yes, some air coolers are so large as to get in the way of installing other components, but without overclocking you do not need to get one of those. If your chosen CPU comes with an air cooler, that will probably be fine for keeping your CPU cool (barring some weird case configuration). The trade off is sound. Default CPU fans are not designed with silence in mind, and when under load can be heard. How big of an issue this is will once again depend on you.
Corsair generally makes good cases, so I do not think you can go wrong with any of their options. However, some are expensive because they are large towers with lots of fancy RGB lighting options and tempered glass. It sounds like that isn’t what would interest you. Consider the Corsair 275Q. It has a minimalist design and focuses on quiet performance, and only costs $90 per their website.
The human eye can definitely feel the difference between 60 hz and the traditional next step up, 144 hz. Consider getting a better monitor as part of the build so you can actually see what the GPU, CPU improvement is delivering. I’ve purchased a VR device, because they are still kind of pricey for not a lot of game support.