Personally, I wouldn't go for a straight "whole house" setup. I'd either want "almost whole house" or just one or two selected outlets.
You don't want the fridge running on AC power when the inverter's on, but using propane. That means remembering to switch it over (and switch it back to automatic) whenever you use the inverter.
You likewise don't want the converter, if it's a separate unit, to run from the inverter power. There's another thing to remember to switch on and off.
If you have an electric water heater element, you don't want that powered from inverter power. A third thing to remember to switch.
What appliances are you interested in running? A smaller inverter would be sufficient for TV and computer and charger usage. A 1000W or 1200W inverter is quite marginal at best for a microwave or most heating appliances (coffee maker or whatever). It seems to me rather a no-man's-land size for most people's needs or wants.