We have flown into Burbank, Long Beach and John Wayne.
Burbank - lovely little airport - awful, awful drive to Anaheim. Will never fly into BUR again - if I'm going to Anaheim - if I'm going to Burbank for something

I would definitely use this airport. We rented a car here for a reasonable price, but hate the drive on I 5.
Long Beach - small, quaint, old - easy drive to Anaheim, we chose to take Katella straight East to Anaheim - took about 25 minutes, even on city streets. Car rentals from here are not quite as inexpensive as SNA, but still reasonable. Super Shuttle runs from here, but costs $35 for the first person and then $9 each additional person. Too pricey for us, so we rent a car. JetBlue flies here non-stop from Salt Lake - so if we can get good fares we fly.
John Wayne - I love this airport - easy on and off freeway access, very close to DLR. Car rentals from here are reasonable and
Disneyland Express Bus and Super shuttle are also available - SS is MUCH more reasonable from SNA than anywhere else, some report about $9 or $10 a person.
We have never flown into LAX and wouldn't unless we were going International - it is less hassle and more convenient for us to fly into a smaller airport that is closer to DLR.