Current Monitoring - CT vs Hall Effect vs Rogowski Coil?
You are correct in that a hall sensor is not as useful for AC currents and if you have no DC offset that is probably not the best choice.

The issue with a current transformer is core saturation.   As long as you can use one with the current range you need that will be your best bet.

The Rogowski coil will work but you will need an integrator to generate the current waveform which usually offsets the additional cost of the current transformer.