150w to 300w inverter is all you need. I do recommend sine wave only.
Use the main 12v connection to the battery for 12v power.
Small transfer switch for each branch circuit you want to power.
Forget powering the fridge and water heater. Actually the fridge is often on the shared GFCI circuit so fridge may need to be set to propane only.
I would keep the 12v marine batteries for now and see how it goes with solar.
15 amp TS $50GoPower 300w sine wave $172 I have this one for lowest idle draw and provision for remote power switch.