I have AC on an input (110V, 15A) and need to control the amount of power going to a purely resistive load.
Thyristor controlled by PWM seems like an option, but are there other/better ways to do this?
It depends what the resistive load is.
If it's a lamp filament, then a phase shift thyristor/triac solution is suitable, as you probably want to avoid flicker.
If it's a heater, with a much longer time constant, then you can use a 'burst fire' controller, to control average power. That switches a number of complete cycles on and off. The benefit of this is it doesn't generate as much electrical interference as switching in the middle of a cycle would.