Accompong,
If you like the BB, then you may as well use it down here. If you want to use the internet options on it other than wifi, then Digicel and LIME offer a slow 2G connection with is rather expensive (you pay by the kilobyte). Claro offers a decent 3G connection, with probably the most extensive island coverage to date. Digicel also has 4G connection option. I would assume you can "tether" your BB to your laptop to use it as your internet connection.
If you need to buy a separate internet connection, both Claro and Digicel offer a UBS connection. Prices for the modem are about the same, and their monthly rates are js$3500 and $3000 respectively. Claro is slower, but they seem to have the largest coverage map on the island. If you are traveling extensively inland, they are probably the best choice.
There is a new player on the block, DeKal's SuperWifi. This is a unique offering as it uses your existing wifi connection with no modem required. It is also less expensive (ja$2000 a month) BUT the coverage area is very limited currently. There are places that advertise their credit (similar to phone credit) but they are outside the actual coverage area. Before trying this one, be sure to turn on your wifi connection and look to see if you see a Dekal or Superwifi connection showing. If you do, just buy the credit and then you will be able to go online without any extra hardware.