I used to do this a lot when I travelled, not so much now that my bag has stuff for my husband now. It is the rural areas outside of negril that need help the most, because they recieve little or no donations from tourists. The best thing to do is to contact the school directly to see what they are most in need of, and how to deliver it. They need the basics- pens, paper, glue, notebooks. You can hire a driver to take you to the school to deliver it. The students have to buy their own tablets (they use the composition books) and backpacks- I recommend contacting a church if you are interested in giving directly to students and not to the school. I don't recommend giving cash as there is too great a chance that the students and school will never see it (this is anywhere in poor countries, not just Jamaica).

Regarding what locals want- urban and sports name brand apparel and shoes(Echo, Sean Paul, G-unit, Nike, etc.). T-shirts are the easiest and best way to go- just make sure you know your brands.
Enjoy your trip.