I recently purchased 2 2000 watt generators for our trip to Alaska which we are presently on. Up here if you want to camp other than a RV park you need the gen's. We do have a normal propane/electric fridge and have had no problems. We have run the gen's when necessary to maintain the batteries and use the microwave and DW's hair stuff and other 120 appliances.
One 2000 watt would take care of your needs with a residential refrigerator and maintain your batteries under most conditions. I purchased two because they are a off brand and wanted to insure if I wanted to connect them they would be compatible, we have spent time in RV parks where storms or other problems have cut the power and having the ability to fully power our rig would be important.