I almost always rent with Budget. I think they are the most professional car rental outfit in Belize, and since they are owned by the same people who own JMA Motors (Suzuki and Mitsibushi dealership) their cars are usually fairly low mileage. They have a location at the international airport (closed Sundays) and a new office on the Northern Highway, on the right as you go into town.
Thrifty, Crystal and Hertz are also pretty good. Just check the car out thoroughly to be sure it has decent tires, a jack and reasonable mileage. There are several "one-person" operations that have high-mileage cars but lower rates and good personal service -- Lewis is one, and some swear by them. Villa Boscardi is also starting to rent cars.
You can get a small Suzuki or similar for around US$65 and up. If you have an Amex or other credit card, it may cover the CDW in Belize, which otherwise is US$10 to $15 a day, a rip off. The 8% sales tax also applies to car rentals.