Our original intention was to go without any form of refrigeration. Specialist boat fridges tend to be very expensive. They use a great deal of power if they run from 12 volts. If they have an engine-driven compressor they cost even more, are difficult to fit, and force you to run your engine every day. On the other hand, a cold drink is one of the most welcome luxuries in the tropics. If you don't have a fridge on your boat, you'll probably end up spending more money, either on bags of ice or in bars ashore. You'll also waste milk and food as it goes off in the heat.
Our cheap solution was to buy a secondhand camping fridge (Camping Gaz CTL175). This cost $50 secondhand, is top opening, and will run off gas, 12 volt electricity or 220-240 volt electricity. The fact that it is not designed for marine use leads to two drawbacks. Firstly, it is going a bit rusty after two years at sea and will need a paint job soon. Secondly, it will not work if the boat is heeled, so it can only be used in harbour, at anchor or when motoring.
The 12 volt setting is not very good - it uses a lot of power and doesn't get very cold. We would only use it when motoring, which is not often in the Caribbean. The mains setting works well on the rare occasions you have shorepower. Normally we run it on gas - which is generally cheap in the Caribbean. It runs from a separate gas bottle to the cooker - a standard Camping Gaz bottle will run it for about two weeks. It's not perfect, but, for the money, it's excellent. We mounted ours in part of the wet locker, between the main saloon and the forepeak. It does give off some heat and does require ventilation, so an opening port above it would be a good idea.