Depending on your needs, I have seen a lot of high end fifth wheels (at shows) with standard household refrigerators. I would NOT limit myself to an AC/DC refrigerator although one that runs off of DC might be a bit more efficient. Don't turn your nose up at 24VDC.
Solar/generator use is hard to say. First of course, is power consumption by the 'fridge and the inverter, if you are using one. If the 'fridge is going to run off of an inverter, make sure it is a pure sine wave inverter. As for a house battery bank, you want a minimum to TWO 6V golf cart batteries. 4 would be better.