[nine_k]

Since the inverter is 3 kW, and the battery is 2.5 kWh, you don't run many appliances off it. Hopefully it shifts your air cooler's peak of consumption away from the most expensive evening hours. You can probably cook at daytime directly from solar power.

When the battery is depleted, you, I suppose, just pull the plug from a battery-fed power strip, and push it into a regular socket.

I would put 3x the battery capacity, which would add about $500-600 to the cost.