And to add some quantification to this, if fan speeds can be kept below 1000 rpm, that tends to be a bit of a cut off point for being audible. Or let's say 800-1000, as a reasonable window to aim for as a maximum. In my new BeQuiet 800 case I've got eight fans going at all times*, with a further four on the twin 970s only firing up when needed, but due to the low RPMs it's basically silent.
Some motherboards will have PWM-enabled fan headers by default, so look out for those as it basically means a similarly PWM-enabled fan will be able to spin at lower RPMs.
Another mildly related point as that you'll *generally* want more air being pulled in to the case than pushed out, too, so you maintain a net positive air pressure in there and limit the amount of dust that can get sucked in through all the tiny gaps. And have dust filters in front of all the intake fans, which higher end cases will come with by default.
*precisely:
1x BeQuiet 850w PSU doing whatever it does standard
2x 120mm front intake @ 700rpm
1x 92mm base intake @ 1000rpm (PSU means this is as large as will fit, and it's only present to try maintain positive pressure)
1x 140mm + 1x 120mm on NH-D15 cooler @ 700rpm (the nice looking but annoying case side panel widget meant one of the stock 140mm wouldn't fit and had to be swapped)
1x 140mm top exhaust @ 700rpm
1x 120mm rear exhaust @ 1000rpm
