Chest freezer as a fridge.
They are much more energy efficient than a normal fridge or bar fridge. They can also be quieter than most bar fridges.
All you need is an external thermostat widget, plug the freezer into the widget, then put its temp sensor in the freezer, set it to the desired temp and you are all set. Apparently they make these widgets for home brewing purposes. They are about $60-$80.
However, I would point out that compressor coolers probably consume less energy still. If you needed more space, though, this is an economical option.
I think I would want a shelf. For shelving I suggest a small upside down cardboard box, and cut away one side, and the freezer already comes with a basket. That seems like it would be about right for my danby 2.7 cu ft freezer.
Some links for your convenience:
(note that this guy: http://mtbest.net/freezer-to-fridge-thermostat.html notes that in a solar power scenario you have to take into account the power consumption of the inverter, if the thermostat itself consumes power, that could prevent the inverter from turning off during periods during in which there is no other power draw. Mind you there is probably always going to be some anyway in a normal house from the microwave or whatever, and the inverters I have seen, at least according to the documentation provided by the mfgrs are highly efficient right down to 0 draw, though there is a good chance they are lying, and that normal inverter technology just can’t really do that.)
It would be nice if mfgrs of chest freezers would tweak their thermostats a smidget so new freezers could do this right off the bat. From what I know of the way they operate, this would be trivial. Heck, you might be able to just reach in there, or maybe it would take some dismantling, and bend the right thing.
They are based on the pressure of the coolant lines, there is a hollow box with a flexible metal side, and when that flexes due to a higher temperature inside the freezer (leading to a higher pressure in the coolant lines), it moves one contact of a switch closer to the other contact. Adjusting the thermostat dial moves the position of the second contact. When they are too close, there is a mechanism (like a magnet) that snaps them together. So by changing the position of the dial, the switch will close when the temperature inside the freezer reaches a certain level, and open again at a different level. Bend something so that second contact is a little farther away than it usually is, and the freezer will operate at a lower temp, for a given dial setting.