The refrigerator is one of the trickiest off grid appliances to maintain. You have a number of solutions, but there are 4 main practical ones.
The first is a “normal” 120vac electric fridge, running off an inverter, and typically is responsible for a large chunk of your power consumption.
The second is a propane fridge, which is friendly to your electrical system (no power, or minimal power for the controls), but requires a regular replacement of the propane, and requires periodic cleaning of the combustion system.
The third solution is a low voltage, energy efficient model, but these tend to be very expensive. These are usually based on the DC Danfoss Compressor.
The fourth solution is also based on the low voltage dc compressor, but comes as a kit (you could also roll your own with a bit of study). A prepackaged and charged compressor and evaporator is installed by you, into a box of your choosing. I suggest a fridge only, as a separate chest freezer (or no freezer) is more efficient, and has more capacity.
Other solutions could include the no moving parts but power hungry peltier cooler, and the converted chest freezer project.