For the First Timers I would bring
Sunscreen - the sun is very strong. Don't get burnt on the first day
Small bills or currency. Not needed at the resort but there are needed when you try some things off of the resort or for bargaining with the locals. They will first try and charge you ten times as much. Bargain them down about 90%.
Under-water or waterproof camera. It will be useful at Dunn's River Falls or snorkeling. If you don't have on the guides at the Falls held on to mine and it did not get wet and they took pictures of us with it.
Water shoes or aqua socks. Again for the Falls and if needed some water sports.
The best advice that I could give first time visitors to Jamaica is not what to bring with them, but what you should not bring. Leave your worries and preconceptions at home. The things you worry about will still be there when you return from your journey, and you'll soon see that Jamaica is nothing at all like the horror story that some person who knew a guy whose cousin once took a cruise ship to Ocho Rios told you.
Have you ever waited for a pint of draft Guinness to settle in the glass ? That's what the pace of life is like in Jamaica. Things might take a little bit longer to happen, but when they finally do it's absolutely magical. And the magic won't happen at all if you rush it. Slow down and savour the moment. Don't plan too far ahead, and don't sweat about all the tiny details for months before you leave. Let yourself fall into the gentle rhythm of the island. At some point, you will find yourself drifting in the warm ocean without a care in the world. You'll have completely forgotten what day of the week it is. Now take a mental snapshot of that very moment of bliss, and carry it back home with you. That is the greatest souvenir Jamaica can give to you.
On a more practical and far less esoteric note, bring pens to fill out your customs/immigration papers. You can use them later to fill out your comment card, and make note of the names of all the Couples employees who helped to make your visit wonderful.
You should bring a couple of blue or black ink pens to fill out the customs/immigration forms on the plane. Fill out and sign both sides (including departure information. There never seem to be enough pens to go around. We usually bring a couple extra for our neighbors.