As mentioned above it boils down to this. To run a house like its on the grid is going to take a big fuel sucking unit. To get by with the essentials a small unit will do.
I'm getting set up for the best of both worlds. A very small unit to handle a base load 24/7 which is fridge, freezers, window A/C, lights, tv, small appliances. I have a backup gas radiant heater so no electric needed for heat. I would run the small unit when I'm gone.
Then I'm planning on getting a big unit 10 or 15 kw. Run it for an hour or two to make hot water and use the electric dryer. After everyone is cleaned up and the wash is dry go back to the small unit.
Big unit 1+ gal per hr. Small unit .25 gal or less per hour. A 2 KW diesel is a real fuel sipper.
If you have a well pump then that load may determine the smallest unit possible. Deep wells can take some juice to run.
Another strategy is to have a large bank of batteries and a big inverter. Lots of short term capacity. Use a military DC generator to start and stop keeping the batteries topped up. A 10KW inverter plus a 3kw DC generator will go a long ways. Just depends how serious one is about the initial cost, the amount of time off the grid, and the expense for fuel, maintenance, etc. It's all a trade off.
Anyway that's my take on it.