We use Budget, also. They're right near the pier and have a complimentary shuttle.
We like to rent a car when arriving a day earlier so we can visit our corporate office, friends, or cruise line offices and Budget is the closest and the cheapest.
46 Cruises & Counting! Favorites: Paul Gauguin to Tahiti: Uniworld River Cruises in Europe; any of the Celebrity Solstice-class ships; Holland America for 12-nights in the Baltics & Russia; RCCL for 14-night Greek Isles, Turkey, & Croatia; Holland America for 14-day Alaska cruisetour; 10-night Canada/New England cruise; 21 days in Hawaii including a 7-night NCL cruise; Oceania for 25 days in Asia; & 3 months touring Europe by train. And many days spent in all-inclusive resorts!