Unfortunately you missed the great sales that all of the best manufacturers of solar generators were having back at the beginning of July, when you could have gotten a 1kwh unit from a great manufacturer for around $500. A 1kwh unit would work great for you. You can use it anywhere inside your house, and therefore don't have to mess with extension cords going through your doors or windows to the outside. Also don't have to mess with gasoline storage either. And if you get a solar panel, your solar generator stays useful even if you encounter a situation where there is no electricity for extended periods of time, and the gas supply goes away. A 1kwh unit can also run a standard-sized refrigerator for a number of hours too.
I would recommend that you look at the brands that use LiFePo4 batteries, which are better than plain lithium for a number of reasons. At the moment, the Bluetti and Ecoflow 1kwh units are around $1k. However, a brand that was pointed out to me here on the OB is called Pecron. I decided to buy their small unit to use in the car with a travel refrigerator. I have been impressed at how well it works, and its build quality seems to be quite good so far. They have their E2000LFP on sale for $849. At the moment, that is the cheapest price for an ~2kwh unit from a manufacturer that I would trust. They also have their 1500wh unit for $699, which might be the best buy in that market right now. But research Bluetti and Ecoflow too before you buy.
Two other brands that have a good reputation is Jackery and Goal Zero, but their prices are often a bit higher than Bluetti or Ecoflow, for no practical benefit. But definitely check their current prices too, as they would be good choices. Anker makes these things too, but I can't tell you anything about them.
Another way to approach this would be to buy multiple smaller capacity units. Two 512wh or four 256wh units will give you flexibility to position them in multiple areas. And if one goes down, you still have another working unit. I wouldn't go as low as 256wh, but IMO two 512wh units would work well for your stated needs. We have two Ecoflow 1000wh units, since we have frequent power outages during monsoon season and we have two refrigerators in two different areas of the house that we want to be able to power if we have a long-term outage. We also have solar panels that we can use to help power one fridge indefinitely (or at least as long as the food supply holds out), should something really disastrous happen.
C