Need super quiet exhaust fan

Again, Nsgarch is correct.
Don't use a metal duct hose to avoid more vibration.
Try www.build.com to find silent fans

If you don't want to hear it, the fan *must* be remote from the room, with generously sized lined ductwork between the room and the fan, with at least one elbow. Use an aluminum or cast grille, not a cheap stamped steel one, at the room, and no damper (dampers generate noise). For 150 CFM I'd use at least a 12x8 duct...the lower the air velocity the less the noise.

For makeup air the transfer grilles, optionally with a filter between, are a reasonable choice. If the space from which the makeup air is coming is noisy, you will want lined ductwork with one or two elbows in it between the transfer grilles. A door undercut would have to be too large to transfer 150 CFM.

Essentialaudio's details/tips are all good ones. You shouldn't need balancing dampers** unless you are exhausting more than one area, or have more than one return grill; in which case balance is achieved by adjusting the size(s) of the different intake registers relative to one another.

** Most externally mounted fan units are supplied with backflow dampers which close when the fan is off (to prevent cold air from entering ;-)

By no damper I was referring to the damper behind the grille. If present it should be fully open, not used to adjust the airflow quantity, and if possible it should be removed altogether. Correct, most domestic fans have backdraft dampers built in at the discharge.

I have 2 remote fans for my equipment closet. 1 for makeup air & 1 for exhaust air. If you want to move air correctly you must use both or have openings to get or remove the air. If you use only one and you have openings it is best to exhaust the air from the top for circulation.