@ShaulaEvans I think you're on the right track in your other comments about wanting to go without. It's also worth thinking about when you expect to use the solar generator. Maintenance and use are important -- it will naturally discharge if left unused for a long time, and that will damage the battery. Also, it's good to be familiar with its use so that you don't have to read manuals in an emergency.
I live in Adelaide, Australia (probably a similar climate to California, or maybe Texas - lots of sun). I have 360 W of solar panels, and 1.2 kWh battery. I have a 650W inverter (for 240V power, the standard in Australia) but it can deliver 1500 W for a short period of time (it's a Victron Phoenix 800, if that's of interest). As another commenter said, this inverter can just start my fridge compressor, which draws about 140W when running, but draws about 1500W when it starts. Some fridges now have soft start motors, which are great because they don't have such a large start up power (my fridge is not one of those sadly).
My system can boil water using a 12V kettle (eg. camping), but I can't run a standard kettle (it draws too much power). I can't cook with it (I have a solar oven, and an alcohol stove that I'd use in an extended blackout), and I think it could run the fridge unless the weather was cloudy in which case it would struggle.
One trick in a power outage is to buy bags of ice and put them in the fridge in a plastic container to catch meltwater. that'll keep the fridge cool without power. (ice isn't always available in an emergency of course...)
I think it'd be very difficult to run an air conditioner on a small system like this. In Australia, many people have whole-house batteries, which I think is what you'd need to run A/C
But it can easily run a radio, laptops, phones, lights, and charge my ebike ;-)
For you, it's also worth thinking about when you want to use it. What would cause a blackout, and would that affect livability (eg. an extended blackout would also affect cell phones, and even possibly water and sewerage_).
A rule of thumb (for Adelaide at least -- your latitude may vary) is that 1 kW of solar panels on average produce 3 kWh/day of electricity in winter, and 8 or 9 kWh/day in summer. But a cloudy winter's day might be less than 1 kWh of electricity per kW of panels...
Hope this is helpful!