A power vented gas water heater with electronic ignition would allow you to put the water heater on a thermostat so that it kicks on when the house temp drops, with any back up like this you would need to install a pump on the water heater tank and a few check valves so it could be automated.
Heating air in a back up situation is going to provide more instant heat then heating up a mass like your floor for quick thermal recovery and quick shut down of the back up.
If you want to go with gas heat, a small direct vent in wall gas heater might be the way to go, 800 sf house is small enough that if it's well designed you could almost go with a heating system designed for an RV.
Other thing to think about is that on a sunny day the south side of your house is going to be the warmest part but on an over cast day the south side is going to be the coolest as the windows are going to give the greatest heat loss, so even adding a base board heater, hot water or whatever source you choose, might be the best way to give your house an even temp on over cast days.
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