If you're flying into FLL, you'll have a hard time finding anything with a shuttle. We've flown into FLL and cruised out of Miami twice. The first time we stayed at the Intercontinental (I got a great rate through Hotwire as a mystery hotel) and we took a paid shuttle service (SAS who I DO NOT recommend) to the hotel and a taxi to the port. It was like $10 for the taxi.
The next time we went we rented a car and drove from FLL to a hotel on the beach in Ft. Lauderdale, then we drove down the next day, returned the rental car to the location closest to port and they had a free shuttle from the car rental to the port. I don't recommend staying in Ft. Lauderdale over spring break. It was a NIGHTMARE. Never again. Ugh.
If I were booking again, honestly, I would just got on Hotwire about a month before, choose something near the port/downtown in Miami and book another one of those mystery rates for the hotel class that fits my budget. All the hotels in the area that I researched were pretty solid. The Holiday Inn is good for a budget (almost stayed there as a recommendation from here) and we were comfortable at the Intercontinental if you have a little more to spend. I wouldn't worry as much about a shuttle if you're close to the port as taxis are cheap and plentiful. Like $10. Or Uber/Lyft if you prefer.