There's "silent" and there's "SPCR silent". SPCR even rates monitors based on the noise they emit (not kidding). It's a great site and resource.
You can get really far with undervolted fans and good airflow (cut away grills, don't use too restrictive dust filters, if any). For example, the Noiseblocker Multiframe S-Series MF12-S1
is certified at 8 dBa at 750 RPM and 34 CFM and you can further undervolt it down to 6V if you want. Normally you won't be able to hear the fan at full speed though, it's just that quiet.