Inverter install idea. We have no inverter

I would recommend that you install an inverter with an internal automatic transfer switch. Magnum Energy and Xantrex have inverters like this. If you want to simplify this even further you can get an inverter that has an internal converter/ charger which would eliminate the stand alone converter. The way the inverters with internal transfer switches are wired is a 30 amp split phase or single line and the circuits you want powered by the inverter would be wired downstream from the inverter. The inverter would be connected to the battery using two 2 ought power cables depending on the size of the inverter 2Kw vs 3Kw. I would use Blue Sea Systems fuses to protect the circuit. The inverter will automatically sense shore power and use that.