Enterprise is the parent company of
Alamo and National but they handle reservations a little differently.
If it were me, I would go with the Alamo rental. You can do the online check-in before you leave home and add yourself, your additional driver and the credit card info that you will be using. Print this out and take it with you. When you arrive at the airport, collect your luggage and then proceed directly to the rental car garage. Pick a vehicle from the aisle that you reserved (minivan), load up and drive to the exit gate (keys are in the vehicle). When you get to the exit gate, present your paperwork, drivers licenses and credit card. The attendant will verify the info, scan the car out and hand you a receipt. You are on your way!
Well worth the extra $16 over the enterprise rental! ****now if we were talking $100, I'd probably go the other way since Enterprise/Alamo/National are basically the same company and share inventory.
It's been a few years since we used Enterprise and at that time they didn't have the online check-in option but they did have the Kiosk near the rental counter where you could check yourself in. When we did this, a vehicle was assigned to us by the system and we were directed to a numbered spot in the Enterprise area in the garage. We didn't like the vehicle so we went to the booth in the garage and they gave us several other options.
Please note that this info is 5 or 6 years old and they may have improved the experience since this time. If anyone has a more recent experience, please feel free to correct/update my info.
Overall NOT a horrible experience but if we had rented Alamo or National we would have been flying along the freeway in the warm Florida sun 20 minutes sooner.