Need to know how many amps your inverter will draw with the CPAP running in order to determine what connection to make and how much battery capacity you need. Remember that you do not want to discharge the batteries more than 50% - i.e half the amp hour capacity.
This is my dual power outlet mounted near the floor between the Propane space heater and the converter:
It is rated for 15 amps DC maximum draw. I tapped into an existing fused circuit.
Almost directly above it is the GFCI 120 volt Master outlet. If you were to mount the inverter in the utility space where the space heater, converter, and water heater are, you could rewire that specific outlet to the inverter output. It would make a simple and clean installation. This would require a new GFCI outlet at the next-in-line outlet box.