Avis. Though I can't speak from experience with the LAX fleets I have never had good experiences with Thrifty or Dollar rental cars anywhere and now avoid them even if they are cheaper. Heck my local thrifty (not LAX) is quite literally someone's driveway with three or four cars parked in it.....
Programs: UA 1MM/*Gold, WN CP/A+, MR Plat, IHG Spire
At LAX there isn't much different between the major rental agencies in my experience. I would choose whichever has the better rewards bonus.
With a flight at midnight I'd aim to return the car at 10:45. I'd allow 15 minutes to drop it off and shuttle to the airport, then 60 minutes to print a boarding pass, clear security, and walk leisurely to my gate. If I were hauling a lot of baggage that had to be checked I might give myself an extra 15 minutes. If I were driving a long distance to get to LAX I'd allow extra time in case I hit evening traffic (YES, you can get stuck in a traffic jam at 10pm in West LA!) or got lost near the airport.
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In general I haven't found big differences between one company and another, except for flexibility in renting, rates, etc. I've used Budget, Avis and Hertz and LAX. I'd rate them all about equal. Can vary by day (determines availability of cars) and the particular person I dealt with. Personally, I'd return the car before 10:45 since the shuttle to the airport could be delayed or slower than you thought, it could run into traffic at the airport (it happens, even late), and I always prefer to have over an hour to check-in, get through security and get to the gate. Jetblue seems to use Terminal 6, so you could have many people getting off the shuttle, with several bags, before you. At thathour, fewer passengers than normal, but several could be international (i.e., more bags). Enterprise gets high marks on the Lonely Planet Thorn Tree bulletin board. I have used them only once, since they don't normally allow one-way rentals and many of my rentals are.