120VAC motor 4watt 60hz speed control -- help

I consider myself new to electronics so please bare with me. I live in the US and most outlets are 110V-120V AC
I was thinking of using an Arduino to create a speed control for an AC motor. I am looking for an easy and cheap solution.The motor is 120 VAC 4watts 60hz.

I know PWM is efficient way of speed control and that is why I am considering Arduino. I was thinking of using a mosfet for the switching but I think I should have something that isolates the HV from the LV so I don't destroy the Arduino. I also have the guts from an old phone charger that I am using to power the arduino.

Also I was thinking of making a full bridge rectifier for the ac to dc. but I am a little confused on the voltage output if I do that. On some forums I've read that the voltage is multiplied by ~1.4 when converted from AC to DC and others I am reading it's divided by ~1.4.

This is not an easy project for a newcomer to electronics. If it's a brushed motor, then it needs a phase angle controller. It it's an induction motor, then it needs a variable-frequency inverter. PWM as generated by an Arduino does not work for AC motors.

Thanks for the reply.
I will probably take a different route for this.