If you've already got a 3 way fridge then it's definitely best run on gas - as Sally says the 12v option is only for when the engine is running.
Trouble is that 3 way fridges are not very efficient and even on gas may have a significant running cost if used continuously.
A 12v electric fridge is usually a lot more efficient but are a lot more ££ to buy; a compressor type(i.e. like regular mains fridge) would probably require about 50w of extra solar into the battery to keep it going, based on my experience of the one I had when i lived on a boat in brighton.
Some 12v fridges are solid-state (peltier) and I'd steer clear of the really cheap ones but I think the better quality ones are OK, but lack personal experience so can't really advise.