Eric,
We have a Xantrex 3012 PSW inverter. I would not recommend a residential fridge on a modified sine wave unit, although you should keep in mind that I am completely at a loss regarding anything electrical. I recommend you do your own research. For information. When we park to boon-dock for a night, we run the generator for a bit (because the inverter has been on since we pulled the shore power at our last RV park) to charge up the house batteries. When we shut if off, we can usually run these things until the next morning on the inverter.
TV, satellite dish, two computers, two charging stations, two C-pap machines, refrigerator, and all of the miscellaneous draws from equipment.
As soon as I start the coffee the next morning, the AGS runs the generator until the coffee is done.