Automatic change over will limit the selection, cost more and is unnecessary. When the RV has AC power the battery charger will supply the DC to operate the inverter, less efficient but no need for any type of switching.
Start with the AC watt load for your devices, add a safety factor even up to 2X for the inverter size. Inverters are generally MSW modified sine wave or PSW pure sine wave. Some devices like a TV may/may not work with MSW.
Also the DC amp draw is about 11x the AC amp draw. Example: A 360W appliance would draw 360/120=3A AC and 33 amps DC. So be aware of the higher battery discharge when boondocking and solar become a consideration.