Congratulations on your upcoming proposal. We have rented cars in St. Maarten a number of times and it is a great way to go. You can rent via the internet and they will have a car waiting for you at the port. You pick up and return there. The island is easy to navigate and if you take some side roads you can find some beautiful secluded beaches.
Orient beach is beautiful and a must see. We usually park at the Bikini Beach Bar (they have a website) at Orient Beach.
Marigot, the capital of the French side is also a beautiful town. Highly recommend stopping there.
Only drawback to renting is not being able to drink if you're driving. Otherwise it is, in my opinion, the best way to go.