Inverters MUST be pure sine wave and 12 volts is preferable (and in some cases mandatory) for some of them like some Resmeds. Common non pure sine wave inverters may burn the CPAP mother board (and will destroy some of them for sure). Check your manufacturer requirements according to YOUR specific model.
Don't expect humidity control (heating) on a CPAP running on batteries. You will drain them in a few hours. Just have the air flow over the water tank.
My wife and I are both on CPAP. We are running them on 12 volts (which is more efficient than on 110 coming from batteries). We have 2 X 6 volts golf cart batteries who can supply the necessary power for 4-5 days.
This set up is perfect for both of us.
P.S. We carry a Honda 2000 generator
anyway in order to be able to charge the batteries if needed. We also have an IntelliPower intelligent charger built in our main electrical
panel. Otherwise I would recommend an intelligent charger connected to the generator