Doug's suggestion would work but it's a bit of a pain to get from the station to the port.
As a 45 yr resident of the Ft Lauderdale area, I'm thinking that the best balance of convenience, cost, and time is to follow Phanatic Luvr's suggestion. That's what i would do in your situation. The Enterprise pickup/drop off policy would fit your needs pretty well.
Another option is to use Park n Go, located right next to the port. They provide a complimentary shuttle service to/from port. Internet only rate is $5.99/day plus tax.