First off I have found booking through Costco to save me lots of money - so if you have a Costco membership look there first.
We have rented a vehicle from LAX for every trip. After you collect your luggage you want to head outside and look for the purple signs showing you where rental car buses will stop for their passengers. These buses will take you to the actual rental car business. There are no rental companies directly onsite at LAX. I cannot speak to any other rental agencies as we always use Budget. If you do use them sign up for Fastbreak as it saves you from having to go in and wait in line - you pick up your car, show your ID and info at the gate and off you go!!
I also found a great route from ludari – as they offered the best route from LAX to
Disneyland: “take the 105 East using the HOV/carpool lane (obviously you have to have two more in your vehicle) to 605 South (don't bother getting in the HOV/carpool lane because it's a short distance until you have to transition to the 91 East (use carpool lane once you get on the 91), stay in the carpool lane because there is an HOV/carpool exit to the 5 South. From that point stay in the HOV/carpool lane and they will be an exit (in that lane) for Disneyland."