welcome to the boards...
i'll try to help a bit
first and foremost, do you have any family/friends on the island? being in proximity to them will make the transition worlds easier... it's a tough place to head without any connections and even tho you are a citizen, you may find yourself treated as a foreigner and you may find everything very foreign... being integrated into jamaican communities in the US helps, but is far from the same...
most jamaicans don't live within a (reasonable) walk to the beach (most who do are in more rural communities and the "beach" is more bush than beach)... if you are sticky on the beach requirement you should be prepared to pay an escalated (tourist) rate (anywhere from 500-1000US a month rent, or more)... if you're willing to be a bit further your prices will likely drop some... i guess it depends on exactly how far you want to walk

getting a room in a house sharing situation is much (much) more economical...
internet is available both thru traditional broadband (flow(limited service, but i believe better quality/reliablity), or C&W in most populated areas), or thru a wireless broadband-type set up in the country... so that shouldn't be a huge issue...
if you want to be "flow"in you need to be in bouge (mobay suburb which would actually offer a great deal of North American convieneces including the Jamiacan version of superwalmart/cosco, megamart... otherwise flow isn't currently offered outside of the Kingston, portmore and mandeville areas)...
from my experiece and understanding, cable and wireless is painful at best but i guess beggars can't be choosers
inet will run you in the range of 3500J a month i believe... you may need to pay a lot more up front to get the installation, esp if the place you choose isn't wired (many will not be).. if you go with a mobile broadband, installation is much simpler, rates are comparable, but bandwidth is capped (can't remember at what at the moment)... claro is probably the best route for mobile connection...
okay, i think that's all i've got right now... hope it helps