I've used Avis a couple time ...
Used Budget once ...
Long time ago used 'Champagne Rental' (I think they're gone now - but I did like the name)
And I've used Island Rental - even bought one of their cars once.
I think they're all fair to use .. but the loss/damage issue and the insurance issue is something you want to get straight before you go down there. If you have a credit card that covers car insurance that is the best avenue. But you need to get that straight with your insurance company before you go ... get something in writing from your credit card company - because their canned response is that your credit card does not cover insurance in Jamaica (or Israel, for that matter). Some credit cards do cover insurance in Jamaica, some don't. The other thing you want to do is go over the car very thoroughly when you rent it ... make note of any and all defects, scratches, tears - make sure each defect is noted in writing/diagram.
I'm with you jasperpro, I don't like the hastle of cabs, and maybe I'm a little spoiled, but I like the freedom of being able to go where and when at my whim. If it costs me a little more .... I just chalk it up to being on vacation ... I'll budget myself on other things, but not transportation. Gotta have wheels, mon ...