Personally, I think a buffet set up in the DR is a recipe for food poisoning, esp if it's going to be out for more than an hour.
But if that's what you want to do, I'd start with an Igloo cooler and make a cut out for a hotel pan. You'd need a supply for ice. If you go with refrigeration, I'd start with the standard beer coolers you see with side doors or ideally, a deli unit. I'd expect to pay about $1000 for the unit, unmodified and used.
Plan on some kind of window or sneeze guard.
In the US, the spec for hot buffet items is they have to be cooked to 150? for most foods(165? for chicken), then held at 135?-140?. Most buffet items will brown with those temps. Anything cold should be held at 33?-40?.
For the hot side, I think you'd do best with rice cookers or crock pots with lids. If you can source an induction cooker, you can put a deep hotel pan onto it as a water bath for smaller hotel pans, like three third pans, if you can find those. You can go really simple with an immersion coil in the bottom in the water, but it will prob burn out quickly, like every other week. You can put it on a dimmer plug to adjust the heat. I think an electric hot plate would be too hard to adjust to the simmer you'd want. An induction cooker would be ideal, but I don't think you could find one down there.