It's assigned. The only ones I know of where you select your own vehicle are Alamo and National. We like being able to select our own car and lately Alamo has the best prices for us so it's been an easy decision.
We rented from Budget (onsite) at MCO last October, and we picked our car. They assign you a car class, but you pick from what is sitting in the garage across from the terminal. If it's really busy, you'll have a limited selection.
I don't know if something has changed recently, but Budget let us pick our car last year.
When we rented through budget last month we were able to pick our car out. We had a selection of cars from what "class/size" of car we were paying for...and we could pick any of the cars in that section.