Renting a car is definately the way to go. We did it last year through one of the big name car rental companies, I can't remember which one, but I did it all on the internet. When you get off the plane, the booths are right there (just outside the airport) and they take you in a van to the car rental place (2 blocks away). Real easy and fast! Lots of people do it. Put it on VISA (just to be safe), but call them before you go just to let them know that you'll be spending all this money. They put a hold on ours because they saw all of this activity.
You will see the whole island this way. Definately go to Orient Beach and Dawn Beach. Eat at La Vie en Rose - get the lobster bisque!!! Visit Maho at night for shopping and drinks. A bar that you must go to is Sunset Beach Bar which is at the end of the runway of the airport. Go before sunset and watch the most amazing sunset over the water while plans land over your head close enough that you could hit them with you beer bottle. Drink Carib beer (like Corona). ........ok, I'm gonna stop now, because I want to go back soo bad. Email me with any questions & I have pictures if you want. Where are you staying?