Count the max concurrent watts you will need and size the inverter about 20% above that, just to give some head room. Your list so far is only 300-400 watts at peak load, so a 500-600 watt inverter would do it nicely. I suggest going for a pure sine model, which should not be too expensive in that size range.
There is no point in getting more inverter watts than you have battery to support, so also consider the number and size of the battery bank. Maybe expand it somewhat if you really expect to do any boondocking.
The big challenge in inverter wiring is making sure that the inverter can never attempt to power the circuits at the same time as shore power. The simple way to do this is to connect the desired circuits directly to the inverter and always run them that way, even when shore or generator power is available. Let the converter/charger re-supply the battery amps as fast as you use them. Many smaller motorhomes are wired in this fashion - it saves cost and is foolproof. Otherwise, you need to add some sort of switching to the circuits , basically a double pole, double throw switch, to make sure they can connect to either shore or inverter power source, but never both at the same time. The wiring diagram to do this is simple, but getting access to the circuits after the RV is built can be a nightmare.