Probably 150 to 300 watt inverter is plenty. Inverter runs off the battery. Solar charges the battery. Driving should also charge the battery and running the generator will(if you have one).
How many watts is the solar panel? Need 100 to 300 watts depending on use. LED lights would also be a big help on conservation. If you have a 12v connector get a USB adapter for the phones.
I recommend at least two batteries for off-grid camping.
I have and recommend a GoPower 300w sine wave inverter. Very low idle draw and a provision for a remote switch if mounted out of the way. A small transfer switch would allow connecting to the existing outlets.
http://www.boatandrvaccessories.com/products/go-power-gp-sw300-12-inverter
