Code states that every element on a circuit must be rated for at least the amperage of the circuit breaker. Since you must have at least 1 20A outlet in a bathroom, most electricians pull a single 20A circuit from a 20A breaker to the bathroom, and then branch off that circuit to a 20A GFCI outlet, lights, fan, etc.
If this is how your house is wired, code states you must use a switch rated for 20A and at least 12 gauge wire for your fan. Regardless of how much amperage the fan draws. This is because if there was a wiring fault at some point between the switch and the fan which pulled more than 15A but less than 20A, the switch would fail before the circuit breaker tripped.
The alternative would be to pull a 20A circuit for the bathroom outlet, and a separate 15A circuit for the lights and fan. If your house is wired this way, you are free to use a 15A switch.
In practice, however, using a 15A switch downstream of a 20A breaker for a hardwired 60W (or whatever) fan is pretty benign. Only you can judge your tolerance for this sort of thing. I would recommend an AFCI circuit breaker (in addition to your GFCI outlet) as a belt-and-suspenders approach.
Really? I think that’s well above and beyond the NEC. NEC is that all outlets and any light fixture within a certain radius of a bathtub or shower must be on GFCI. But other fixtures (including above a sink) GFCI is optional.
Or at least that’s the way it was when my house was inspected 2 years ago… I should go back see if it’s been updated.