For powering up stuff inside you have several choices.
You can put ina propane gas system for your stove, heat, hot water, and fridge. This is what most RV's use.
You can go all electric with a mix of 110-VAC or 12-VDC, all 12-VDC, or all 110-VAC
Each has good points and bad.
You have already identified your basic power needs. 1200 watts is not going to be suffcient to effectively power your needs. 3000 watts would be more sufficient.
If you coupled your 1200 watt genset with a battery bank and an invertor/convertor you wouud be right in the neighborhood. You could then supplement the genset with a solar array that would allow you to go quiite a long time between genset runs or tethered to the grid via a power cord.