I built up a silent PC by swapping out the CPU cooler for a nofan one and a low noise power supply. It's entirely silent but I did have to consider the processor as it only has passive cooling. Getting rid of the fans means the case isn't too important so long as it has a lot of ventilation.
Anyone had luck with quiet/silent PC cases? I would like to shut mine up a bit. It’s an ATX board in a very old case.