Lui, we were just there a month ago and had arranged a driver for the day (he was also a bodyguard). If you go on your own, you do not have to contend with long lines, and lines actually climbing the falls. But if you go through your ship, you will be able to get some good quality pictures of yourselves because the ships photographers are usually there when the ship passengers climb up.
You really should be careful making your own arrangements on shore. We always go off on our own but do not in Jamaica because of the safety factor (plus we had our kids with us 6 and 7 yrs). Branch managers of foreign banks in Jamaica have personal bodyguards and drivers, so when we went down the branch manager's personal driver/bodyguard knew who I was and picked us up from the ship and drove us around all day and took us here and there and negotiated rates etc for us in shopping areas and beach rentals etc. If you like, email me and I can give you the drivers number in Ocho Rios and he can possibly set you up beforehand with a taxi driver whom he trusts. (that's pretty safe).
We have done it both ways and prefer to do it on our own. If you do it on your own, get the price of the fare to the falls before you get in the taxi, it should be around $5-$6pp round trip. Make sure this is for a round trip as well. You will pay the taxi driver AFTER he meets you back at the falls at the time you set with him. Entry to the Falls is I think $10pp. You can watch the others to see where the easiest way up is or just wing it. <G>
Stay out of the straw market at the top of the falls, they are very, very pusht and rude there. The Straw Market downtown is better and while they are hard sellers, they will treat you with respect if you treat them well and honestly.