Here's what I did:
a) Rubberbanded scenario-specific cards (objective, event, clue) for easy separation.
b) Extra compartment for the small cards, except one for "misc" cards, you know, time eras from FA for example.
c) Everything investigator-related in a seperate box, deliberatly unsorted. That'll keep the investigators busy while the keeper sets up the board.
d) Each puzzle type in its own ziplock bag.
e) Sorted out all story choice markers and sealed door markers
f) Sorted exploration cards alphabetically.
g) Monster seperated by type in their own compartments.
But that wasn't even done to speed it up, mostly to make it more convenient.