This is a subject that is very close to my heart - quiet cooling..
My pc runs stock at:
CPU: 31-32C (idle) 39C(load)
System: 24-25C
PWM: 28C
And i am running:
2x 80mm Vantec Stealth Fans @ 21DB
480W ThermalTake Silent Purepower (fan controlled - on low setting)
Akasa Acoustic Matting (surrounds the edges of my case fans, harddrives and cdroms to stop vibration and is on the bottom of my case, and all side panels)
Artic Freezer 64 HSF @ 16-21DB
My case is literally inaudiable.. its almost completely silent, when i say almost the only thing making any audiable noise.. is my graphics card (6600GT) which has a rather loud HSF on it (retail). Just waiting for Artic Cooling to bring out a silent HSF thats compatible :)
Get a case thats good quality = reasonable weight, this means that it wont be flimsy, as if it's flimsy you will get ALOT of vibration.
Which ever case you get it will most likely have "grills" at the back and front of the case to basically protect people from shoving their fingers in the fans..
If you think its safe, ie no small children e.t.c cut these grills out, it looks unneat.. well mine does anyway, (i've done it at the back of my case) with a simple wire cutter, it will lower the db of noise the fan is making, as there are no metal grills in the way blocking the air flow..
Wiring is another thing, try when you build you computer to make sure that your powersupply connection (20ATX and 4ATX cable are not situated above the HSF, as this will partially block airflow out of the case.
As for other wiring, such as IDE cables / Case (front panel) wiring, try to hide it in the side panels, behind the IDE compartments or under the motherboard, it can take a good few hours to get it right but it is worth it :)
If your using IDE cables buy some Akasa Rounded cables, these are as you may have guessed.. Rounded IDE cables, which are quite small and very neat, they make the system look alot better and provide much better airflow.
Hope this helps :)