[Wavery]

I have basically the same set-up that you have (230ah LiFeP04 - 400w solar)

I would recommend a 2000W pure sine wave inverter and forget about running your air conditioner. 2000W would allow you to run your microwave for about 5-minutes a day and coffee pot once or twice. I would not recommend getting anything less than 2000W. You will regret it in the long run. Just because the inverter is 2000W, that doesn't mean that it draws 2000W, it just means that it CAN draw 2000+W, depending on your load. It's better to have it and not need it than to need it and not have it.

I installed an ATS (automatic transfer switch) so that when the inverter is on, every 110V outlet in the camper is active (except the converter's charger). When I plug into shore power, the power from the inverter is shut-off and all of the outlets are live through the converter (including the converter's charger).

If you don't want an ATS, you'd be wise to just run an extension cord from the inverter to the devise that you want to power. Otherwise, you run into complications like burning up your inverter when you hook to shore power.

Check out the pic of my wiring. Take note of the wire sizes. Very important that you do not go any smaller on the wires with a 2000W inverter. BTW, I run a 110V dorm fridge (4.5 cu ft) 24/7.