How to control RPM of an AC motor with minimal parts
1) Simply add a resistor in series. This will drop the voltage supplied, but likely increase current draw on the windings?


When driving a fan with a shaded pole or permanent split capacitor (PSC) motor a variable resistor is the simplest way to reduce speed. It will reduce the voltage  and reduce current slightly rather than increase it. It will reduce the power used, but not as much as other methods.

The capacitor switching method is explained in more detail in my answer to the following question:
varying run capacitor for speed control of single phase motor


  2) Add some capacitance some how to adjust the power factor of the motor to increase/reduce torque?


That may work somewhat like a resistor, but selecting a value will be problematic. The speed will not be adjustable. It has been done commercially with PSC motors, but I don't think with shaded pole motors. There is a three-speed switch offered for this fan. That is probably a capacitor switch for a PCS motor. If this is a PSC motor, its capacitor(s) could be quite small. With capacitor switching, you typically get three speeds.

For the fan you have, you probably need to use either a resistor or triac voltage reduction method or buy what the manufacturer offers. When the fan is sold without the speed control, the capacitor is probably buried inside the motor housing with no external connection for switching capacitors.


  3) Triacs to chop up the wave form to reduce the ON time the motor receives.


True. That provides a continuous range of speed adjustment. It provides more power reduction than a series resistor.