Most people get to & from in small busses, or taxi cabs.  Most people have transportation to & from the airport arranged before their trip. Traffic is always busy especially on any route to & from the airport due to the fact that flights are arriving/departing all day, and people are being driven to their destinations.

 If you are staying at a large resort, resort provided/arranged transportation is usually an option.  You can arrange for rental cars, mini-vans, or taxis in the airport after clearing customs.

A lovely benefit of some of the large resorts is an arrival lounge, often kept cool with air conditioning.   It is a great relief after the hastle of customs to sit and relax a bit while the staff handles your luggage and arranges for your transportation to the resort. 

A tip for families coming through customs, try to catch an official who is managing the lines.  They will usually direct a family with small children to a short line or one that is designated for returning Jamaicans.  It can save you up to an hour in line and just shows again how much Jamaicans love children!