The CFM of an exhaust is based on how many air changes per hour you want. If your ceilings are 8', you have 1600 cuft, so your rule of thumb 1CFM per sq. foot would get about 7 air changes per hour. I don't know if any codes address this, but I believe numbers between 5 and 8 changes per hour are tossed around, so you are in the ball park.
A single fan of 200 CFM, or even 150, will be noisy. Panasonic makes probalby the quietest; I think they have a 0.8 sone 160CFm unit. It is pricey; around $260 last I looked.
I would consider a remote inline duct fan, or even 2.
In most areas, having windows in the bathroom meets the code ventilation requirement. But your experience is typical: the windows are never opened!