Anyone going off grid needs to consider their fridge.
The ideal fridge for a stand alone power system has lots of insulation, a modern compressor, upright ease of access, and large usable clear drawers to prevent cold air falling out when opening the door.
It would come in a range of sizes from 100L to 500L and cost only a little more than an equivalent inefficient 'normal' domestic model.
Unfortunately, it does not exist. So we need to accept that there will be some compromise.
This compromise is between price, efficiency, and convenience.
The biggest change in fridge technology recently has been the move to modern digital inverter compressors. These were pioneered in air conditioners and allow the fridge to run at variable speeds. Traditional fridge compressors started hard, and went full speed and then stopped when the fridge got cold enough.
The digital inverter compressor winds up slowly as needed and dramatically reduces the size of the stand alone battery inverter that is required. A traditional fridge alone would require a 1000W or more to start up. Digital Inverter fridges (commonly sold by Samsung and LG), require as little as 150W.
These fridges are sold to the mass market and therefore very well priced and easily available.
3 way fridges (12VDC/230VAC/Gas) are NOT recommended. They use an evaporative cycle instead of a compression cycle and heating with electricity requires a lot of it.
'Gas only' fridges aren't usually recommended either. The ongoing gas cost is high, and there are risks of exhaust poisoning or fire if they aren't properly installed and maintained. They also tend to become less efficient as it gets hotter, when you need the fridge the most.
Chest style fridges and freezers are very energy efficient and typically have more insulation. However the usability suffers and they still require a larger inverter. You lose the vertical space of an upright fridge and things tend to get buried down the bottom over time.
If you only want to have small batteries and run the fridge through the day, this is the way to go, as they are more likely to stay cold overnight without a boost.
For the energy efficiency enthusiast there are some modification projects that can give you a more efficient fridge than is commonly available on the market, perhaps Peter Pedals can write in with a follow up article that goes into some more detail.
So there are options for special cases, but for the vast majority the Samsung/LG 250L or 350L are the way to go for the balance of cost, power (watts), energy (watt Hours), convenience and appearance.