I don't know what kind of answer you're expecting.
I want a case that will be quiet and also keep components cool.
This is what pretty much everyone is looking for. Rather than ask on here, your best bet is to go to YouTube and watch case reviews from channels like Linus Tech Tips and HardwareCanucks. Search any case and you can bet on both of those channels having a great review.
If you want a quiet case, take a look at the BeQuiet! Base 800. Or just look at OverclockerUK's
entire section of noise-dampening, both pre-dampened cases and dampening kits for existing cases.
Cooling relies almost entirely on your cooling components. I recommend both BeQuiet! and Noctua for quiet CPU air coolers. Or buy a water cooler (like an H100i) and get quiet fans (again BeQuiet! or Noctua are good for this). Again, just look up reviews on YouTube for "quiet pc cooler".
I'd avoid mini-ITX cases, just because it's more difficult to build a quiet system, and harder to get coolers to fit inside. You probably want a midi or small tower. I like micro-atx personally, but again, just watch some reviews and buy the case you think looks best. Then buy the cooling components that the reviewers say are effective and quiet; they'll almost definitely be BeQuiet! or Noctua.
tl;dr: get a
BeQuiet! Base 800 unless you're in the "it looks like crap" camp, in which case buy
one of these.