You could get by on two batteries if the sun is good every day or you have a small generator to use if needed. Otherwise with a few cloudy days and no generator I recommend 4x GC2 (golf car batteries).
Again 200 watts solar will work great when conditions are good. 300 to 400 watts would serve better when the sun breaks out after a few bad solar days.
Solar controller keeps the battery charged. Inverter will supply 120vac from the battery. I have and recommend the Go Power 300 watt sine wave inverter for the usage posted. Very low idle current and has a provision for a remote power switch.
Price and compare 12v panels at the Isc rating (short circuit amps) not wattage. High voltage (24+v) panels are lower cost, physically larger, and require a higher cost MPPT controller. Make sure the panels will fit properly with 12 to 18" spacing away from shade items like air conditioner, open vents and antenna. Even small partial shading can cut power significantly.
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