Get an Antec sx830 or sx1030, and some wimpy, quiet fans like 80mm PCP&cooling silencers, L1a panaflos or some of those quiet Addas(?)
Depending on your system, you may only need 2 blowing out the back, or 2 in/ 20ut.
The sx antecs have temp controlled psu fans and very low resistance to airflow, so you can use weak case fans. The loudest part will be the PSU fan, in all likelihood.
Once you have a low restriction case and quiet fans, you can try sound deadening/vibration dampening materials. They don't do a lot, but the difference is noticeable in already quiet systems.
SX antecs