Bubba1 is right on here. Anything that is going to require heat is better supplied with propane. Buy a propane camping stove that you can connect to a 5 gallon barbecue tank.
Your real priorities should be lights, communications, and refrigeration. To keep the lights on, the refrigerator running, and maybe an hour or two of computer/TV time, I'd guestimate you'll need around 2.5kWh of power. That is very doable on a solar system, but it NOT a trivial amount of power.
Assuming you need 2.5kWh of power in the middle of winter, with 2.5sunhours of light, you'd need about 1000W of panels to accomplish this. This power level typically would require a 24V system.
Let's say you want 2.5kWh of power per day, and need 2 days of autonomy for 1 day of cloudy weather. Assuming you don't want to drain a deep-cycle battery more than 50% the math works out to be 2500Wh X 2days X 2Xbattery capacity = 10,000Wh of battery capacity. At 24V, that would be 10000Wh/24V =417Ah of battery. Look at Trojan L-16s for that power level.
So, what do you need?
420Ah of battery at 24V (or maybe 300Ah of Li battery)
1000W of solar panels (1500W might be better for this size battery)
24V capable charge controller 40+amp (60A for 1500W of panels)
24V inverter, maybe 2000+W (A 3000W AiO might replace the charge controller and inverter)
It's doable! Start shopping.