What capacitor and resistor to use in my simple circuit?
The motors used in those kinds of appliances are typically "universal" motors, which are basically series-connected (armature and stator) via a set of brushes.

The capacitor is there to help keep the electrical switching noise of the brushes from feeding back to the line cord and radiating into any nearby AM radios. It may or may not be effective at this.

The resistor is there to discharge the capacitor. Under some circumstances, the brushes on the motor might stop in an "open circuit" condition, and if the power switch is opened near a peak of the AC waveform, a significant charge can be left on the the capacitor. This could become a danger if the appliance is subsequently unplugged and someone touches the prongs of the plug. So the resistor bleeds off this residual charge in a reasonable amount of time (a few seconds at most).