Here's what I've purchased:
ExpertPower 12 Volt 50 ah Deep Cycle Sealed Lead Acid Wheelchair Medical Mobility Rechargeable Battery. I really like this battery as it has bolt style terminals and a handle. It is an AGM battery. While I wanted something that would last longer, the 50ah batteries were about as heavy as I wanted to move around. In my test at home the battery lasted a solid four nights with the humidifier turned off. I'm using someone's trick here of using Ocean nasal spray just before bedtime and in the morning (I didn't miss the heated humidifier).
At a pressure of 10cmH2O, I think my machine needs 12 ah for an eight hour night, so a 50ah battery should last for four nights which it did. I believe it would require a 60ah battery to make it the full five nights but that was just heavier than I wanted.
BatteryMINDer Charger/Maintainer/Desulfater - 12V, Model# 2012
If I had it to do over I would buy the AGM version of this charger but this one seems fine, it charges normal AGM batteries like mine but not the specialty or higher end batteries like an Optima. It recharged my battery after four nights use in 3 hours. It's easy to use and a quality product.
ResMed's converter for the S10. The converter worked well other than the connection between the cigarette power adapter pieces was a bit fussy. I found to check that connection first if my machine wouldn't power on.
Anyway, that's my experience so far with a battery backup. Hopefully it will help someone. By the way, I didn't push the battery to go five nights as the batteryMinder, when I attached it to the battery after the 4th night, told me it was running low.