While it sounds like a great idea, and actually is for a survival situation, one would need a good-sized battery bank to power things like a fridge or A/C or furnace. Motor loads burn up a lot of power, thus batteries would get drained pretty fast.
You have to do the math calculations to see it, but generally, power in has to equal power out. Example; If a fridge requires 1500 watts/hr at 120 volts for 10 hrs, then it needs 15,000 watts total. You will need a battery bank that can supply that wattage, while still maintaining it's voltage at something greater than 12 VDC. Add to this the intrinsic losses converting that 12VDC into 120 VAC through an inverter, and you need to add a "fudge factor" to the total. Since power in watts, divided by volts equals amps, then 1500/12 = 125, then you need a battery bank that can supply 125 amps per hour in order to power that fridge for just 1 hour. Now, if you need to run it for 10 hours, then it becomes a daunting task to expect that bank to supply that for ten hours. Realistically, the fridge compressor won't be running the whole time, so the numbers I just gave are more than actually required.
From a purely practical viewpoint, the gas or propane powered generator is THE way to go, and you don't truly NEED one much larger than about 5000 watts. That will supply your house with about 20 amps at 240 VAC, and if you're judicious with what you attempt to run, then survival mode is quite attainable. There was a time when I lost power for three days, and I lost a BUNCH of food. (At the time, I was powering two fridges and two freezers, plus needing a furnace and minimal lighting.) I got myself a 6.5K generator and never looked back. I have lost power since then, and unplugged a fridge and freezer for a day, then alternated between the pairs to maintain temps.
My recommendation would be a propane generator, as a gasoline or even diesel one has to have a standing fuel supply, and both gas and diesel gets stale, can dry up out of the carb (long term), thus requiring one to service the generator not less than every year. It would also be quite wise to start and run the house on that generator not less than every 6 months.
Now, I'm not saying a solar system and good-sized battery bank won't work, but one will have to plan it out well, and one would still need a small standby generator for those times when it might be cloudy for a week, in order to charge your battery bank. (Like during and after a hurricane.)
BTW.....forget the laptops, TV and internet during those times. Even that miniscule amount can add up, and there's very little that you really NEED to look at online that will help you survive an emergency situation. The phones I'll concede, a fridge, a furnace, a few lights, and that's about it. You don't need to run the A/C....draw a cool bath or shower of you need to cool down. If you have DETACHED garage, run the generator in there, back-feeding through the garage's electrical system. That way, you can lock the garage up and maintain some modicum of security for your generator. (Yes, your neighbors will steal your stuff in an emergency situation.)
Roger