The main fridge on my boat is a 3 way propane unit. It works very well keeping things cool especially with the additional 12v muffin fan to help vent the heat out from the coils - I run this fan constantly when the fridge is on, it uses less than .1 amps. The fridge is installed per ABYC with proper pan and 'drain' overboard. I carry 3ea. 20# propane cylinders which last the entire summer, also cooking and heating water with propane. Just had a full, out of water insurance survey last May and everyone is happy.
Additionally, I have a WAECO 12v/120v Danfoss cooled 'freezer/refer' which is kept on the cockpit during the summer's cruise, usually 60 days. We run this on 'freezer' mode and pack it with less expensive food from the states before venturing into B.C. where all food is more $$. As we use the food, the empty space is filled with ice cubes for drinks etc. The freezer is pretty big at 2.8 cu. ft. and this unit will consume around 80-100 amp hours at 12v.
So, we have both cooling methods aboard - 'scary' propane and electric - both do a great job keeping the ice cream cold.
On the original posters question on battery charger size, you need to determine what the normal daily amp hour use is on board. This will tell you exactly how long your house bank can get you before needing a recharge.
Whether you recharge with your main engine alternator, or a genset or solar panels or windmills is a different question and requires some thought on how you actually use your boat while cruising.
In our case, we may be dockside during the 60 day summer cruise 3 or 4 nights, so it is important to me that we can live on the hook for a long time. Actually my house bank is sized to allow up to 6 nights at the same anchorage before needing to initiate a recharge cycle. I don't have a genset, instead the engine alternator is a large frame 200A unit that does a super job of replacing used amps in a surprisingly short period. Since we drive the boat anyway, why not use the main motor to recharge the bank?
In practice, we often stay 2 nights at the same anchorage, and regularly 3 nights, but have not yet stayed more than that. I suspect the holding tank would fill up before 6 days would pass anyway.
good luck