To control motor : 1phase, 230 V brushless, via RaspberryPi
For a fan load that requires only 135 watts, a single phase induction motor with a variable AC voltage would be least expensive alternative for continuously adjustable speed control. A split-phase, capacitor-run motor would be fine. A shaded-pole motor would also be ok. A split-phase capacitor-start motor would not work, because the capacitor might not disconnect when the motor is started or might re-connect when the speed is reduced. A split-phase motor with unspecified starting method would probably be a motor with two windings of different inductance and winding resistances. If you could find such a motor, it would probably work. Such a motor with a switched winding would not work.

For additional information about controlling induction motors with variable voltage, look at: Speed control for PSC induction motor.

A universal motor would work, but they tend to have much higher speeds than induction motors.