I've been told this is the best option:
Southern California Gray Line - Airport Information
EDIT - as a few members already pointed this out ... there you are with the website. Book it! This option can't be beaten. I actually got this tip from another website .. recommended from David Michael - "Darkbeer" himself .. who I consider the best "Walking Disneyland Trip Adviser" out there.
$20 dollars one way
$30 round trip
Either runs every 30 or 60 minutes.
Call them ... find out EXACTLY where you pick it up on the LAX driving loop. It can be very confusing ... don't hesitate to get specific information where to pick up.
Forget about el-cheapo route Green Line to the Norwalk station and busses. Carrying a lot of luggage .. on public transport ... plus the Green Line stops along infamous sections of LA County .. such as THE BELT (Compton, Watts -- You get the picture!!).
The Grey Line Disneyland Express is your best bet!