My twenty year old house has cheapo ceiling exhaust fans that clang
and make all sorts of weird noises but they still work! If I were an
Engineer calculating the fastest way to exhaust "foul smelling
bathroom gases"...what kind of exhaust fan would I buy?

I would think running the fan for thirty seconds after the occurance
of foul smelling gases should be quite a sufficient amount of time for
a well planned exhaust fan to rid the bathroom of noxious odors!

Bill