There are plenty of flights to Jamaica out of the UK from airports across the country, so check around for the best deal. Jamaica has two main airports, Norman Manley International Airport serves the capital Kingston and Donald Sangster International Airport is in Montego Bay, so it's best to do some research about where you want to go before you book flights.
There is no public transport that serves either of these airports, but if you're staying at one of the resorts then shuttle buses are generally provided; check before you travel. Car rental is available and is a great choice if you want to see some of the country under your own steam. Taxis are easy to get too if you want to get travelling without too much fuss.
Driving is a good way to get around and get some freedom, although be careful as the roads in Jamaica can be poor and driving erratic! However there are other ways to see the island. Local buses offer extensive routes all across the country and large luggage is accepted too, just remember to tip the driver for lifting it! Tourist taxis are very obviously taxis and will get you around but at a high price, a cheaper option are the local taxis, often called route taxis. Favoured by locals, route taxis can be spotted by their red licence plates or spray-painted signs. They charge a fraction of the price, just don't expect to have the taxi all to yourself!