I believe the least expensive way and also the most convenient way for the transfer is simply to grab a taxi. That is what I do and it seems to work the best. I have used Super Shuttle as a single, and while it is less expensive (for 1 person) the hassle doesn't seem to be worth it.
I have reseachered this a lot on the boards and the web and have found that carnival to be $32 a person. Then you have to wait for others to fill the bus before they leave the airport. Then on the return you have to find the buses that are going to Ft. Lauderdale airport and fight with everyone else that are tring to catch the same bus. If you have time constraints with a flight leaving early you are gambling on catching the bus and getting to the airport on time.
I have found the securing a shuttle or Limo is cheaper and faster and more personal. I am traveling with my family of 8 and the Limo is $80 each way $160 round trip. The limo driver will meet you and take you directly to the port. The on return will meet at the port and take you directly to the airport.
So 8 passengers the carnival way times $32 equals $256 almost $100 cheaper than the Limo. Just my 2cents on the matter.
Car rental - I would think that would be cheaper than shuttles or taxi. I did an Avis - Your Base Rate ( 0 day 5 hour / unlimited mileage ): 61.99 USD. If you have a particular favorite rental company. i would do that.