Schools worth considering include St George, Ross, and even AUA. These three have a good residency match rate and are more structured and have better affiliations with the USA hospitals for doing clinical rotations at good locations.
Any other school will be a gamble, trust me, I graduated from one of these random Caribbean schools.
But do keep in mind that as a Carribean Medical student you will be limited to the specialties of Family Medicine, Internal Medicine (and IM subspecialties like Cardiology), Pediatrics, Pathology, Psychiatry, Surgery, and possibly Anesthesiology.
Regardless of which Caribbean school you go to, if you are unable to get decent USMLE scores, it will be hard to match into residency.
Also if you're a US citizen you will have an advantage of not needing VISA, I'm guessing the OP and most of the people here are US citizens (this is a decent advantage to have over other IMGs). Me being a Canadian Citizen, I have to compete with non US IMGs from India, Pakistan, China who have 250s and 260s on their steps.
Don't let living conditions in the Caribbean deter you, you will only be spending 2 years on the island, that's very short term and time will fly. Your rotations will be in the states.
My suggestion would be; Apply to US MD schools and US DO schools, and if you don't get in the first year or second year, then go to a Carribean school. Again, SGU, Ross, or AUA.(maybe there are other higher tier Caribbean schools that I can't think of right now).
Not only do other schools like the one I went to have a bad record for matching (although plenty of my classmates are in residency currently), but these schools are infamous for pinching money out of students including my school. My school would spring random fees last minute that we were forced to pay, and those who didn't want to pay were not given their transcripts so it was impossible for them to transfer our until their payed their balance. I don't think situations like these would happen in schools like St George or Ross or AUA as they're more organized and reputable and have multiple share holders etc. not just one single tyrant as their school owner. The higher tier Carribean schools are more expensive overall but there's more reliability.
Note: I can't overemphasize the importance that board exams play in getting into residency. the biggest hurdle you will face as a Carribean student will be studying for the USMLE step 1 and step 2CK, and IMGs take months and even sometimes years to study for their Step 1, and many of my colleges were unable to get through their Step 1 exam (some are studying for 2+ years but can't get through their mock step 1 exam required before taking the actual Step 1 exam), so if you work hard and get good scores you will make it. But if you don't do well on your steps there's less opportunity to redeem yourself than if you were an American Medical Student. A failure on the step as a Carribean Student is career suicide(with some exceptions, I know a few who overcame this and matched). Compare that to a failure on the step of an American Medical Student, who will still match into a residency(maybe not the location or specialty of their choice, but they'll get something).
Those were my two cents about this issue. If you really want to be a doctor and theres no other way, go to a reputable Caribbean school.
PS. I'm a graduate from a Carribean medical school that isn't the top 4, passed all my USMLE exams with mediocre scores, I'm a visa requiring applicant, and I'm going to be applying for the second time for residency for the upcoming 2020 match in Internal Medicine and Family Medicine.
Edit: My mistake, the big 4 Carribean schools are: SGU(St George), Ross, AUC, and SABA. AUA is pretty legit as well.