If you want to go the non-lithium way, you will probably want an AGM deep cycle battery. AGM is a lead-acid battery, which in theory could offgas, but probably won't be an issue. You don't need to add water - a very nice feature and it will not spill if knocked over.. You want a "deep cycle" battery...

I have a toy hauler with four 6-volt batteries wired to provide 12-volts and about 460 Amps. Recharged via generator or solar. My wife and I both use ResMed Aircurve 10 machines. We each have the ResMed OEM DC power cord that takes 12-volt house power to 24-volts. Assume we plug into 12-volt sources...