I am from the DR..

cherry of the rio grande would be my choice

Haven't tried rose apple but i have tried the cashew in my country, dominican republic. the fruit part is awful, you would not like it and it comes with only one cashew. I would not buy a cashew tree

I tried everything from bagging them to trying to poison them with no avail.. the only thing that seemed to work was to cut it's life cycle..
the papaya fruit fly inserts an egg into the papayas on the tree, the egg becomes a larva that eats the seeds inside the papaya, it rots and the papaya falls to the ground.  then the larva gets out of the papaya, digs a hole in the ground  where it matures and becomes a fruit fly and repeats the cycle. you have to cut the cycle.. when you see that the papaya, on the tree, has been infected.. discard the papaya, throw it out, away from the house so the larva never becomes a fly.. if you have many papaya trees, it might be hard to prevent one of the papayas to fall to the ground but that is what you have to do.. papayas should never fall to the ground, that's where the larva matures into another fly..

cherimoya would not grow in northern Florida as other have said.. it does not tolerate cold temperatures and will kill the plant.. try growing peaches, apples, figs, blueberries..