We have started to become rather loyal to National, so I would recommend joining their Emerald Club and booking mid-size cars (that way you get access to the Emerald Aisle, where you choose your car from a selection that quite often includes vehicles far above "mid-size").
With LAX all the rental agencies are offsite, and involve a shuttle ride over to the particular rental place. The terminals are well signed for where to wait for what shuttle.
I don't remember the route from LAX to Disney, but it was fairly simple especially if you have something like an ipad and navigator in the car with you.
If you don't need the car in the middle of your stay and don't want to pay for parking, you can book the car as a one-way rental, and drop it off (I recommend) at the Alamo/National (assuming you booked Alamo or National!) location next to Alpine Inn on Katella. They have a shuttle to take you back to your hotel (and pick you up, I assume) that was very helpful.
But you have to do the figuring to see if keeping it the whole time and paying for parking is better or worse than a couple short-term rentals.
Even though they are usually WDW-centric, there are always loads of car rental threads on the Transportation forum. That way you can keep track of codes and coupons for various rental companies. I like mousesavers.com to keep track of those things, too. And remember that rental companies change their rates ALL the time! Our trip to Orlando is 12 days out and I fully expect that rates are going to change inside a week. (knock wood) I have my records from previous trips and I often change my rental codes/coupons just a week out. So don't look at things once and decide it's too much, etc. It can change. But you have to check and recheck often.
