I think your solution is very simple. Buy the Honda 2000, and run it when you need it. After buying an inverter ($200), you will discover your battery is too small. After upgrading your battery/ies ($200 - $400), you will discover you must charge them. Then you will discover you need a smart converter/charger ($150) for the battery/ies. Could go with solar (about $800-$1000) which works great with the sun shinning, but will not run your microwave or A/C.
I have an AGM battery, smart charger, solar and a Honda 2000. If I could only have the Honda or solar, I would take the Honda. The biggest Inverter I use is 200 watt, that plugs into a cig socket. The $1000 Honda will do everything you need, and more.
With one 100 AH AGM, and 130 watts of solar, I only need to start my honda to run the microwave or A/C. The solar does everything else, without an inverter over 200 watts.
Wayne