A big factor in this equation is what airport you are planning on flying into. Three airports service the immediate area (LAX, SNA, and LGB). At SNA and LAX, you have more options (namely, the Disneyland Resort Express). Keep in mind that, while WDW has the Magical Express, DLR has no such thing, and all transportation is your responsibility to coordinate and pay. The Disneyland Resort Express is *not* ran or owned or even endorsed or recommended by Disneyland.
Your three qualifications are: safety, ease, and price. There are three typical ways to get from the airport to the hotel: a hired vehicle (shuttles, limos, etc), a rental car, or a "drive-by" shuttle/bus/taxi. Safety-wise, the Disneyland Resort Express may be the top in safety and ease of use--it's a huge Greyhound-style motor coach, and doesn't require the use of child restraints. In fact, there aren't even seatbelts! Safety is maintained through "compartmentalization," just as in a school bus. If an accident occurs, basically, you won't go further than the seatback that is in front of you. The unfortunate part about the Disneyland Resort Express is, if you are flying into LAX, you are stuck waiting on a center island with vehicles going around each side of you.
For ease, I'd think a hired car would be at the top of the list... They will often wait for you in baggage claim and help you with your bags. Of course, if your children are young, you would need to provide child restraints. (I would personally never expect a hired car/shuttle to provide correct seats--seats expire, need to be cleaned specific ways, and not all restraints fit all children; that's a lot to trust to a hired car driver, who could well be a 22yo single man who hasn't ever used a car seat.)
Regarding price, that's highly dependent on what airport you are flying into... A taxi from LAX is approximately twice as expensive as a taxi from SNA or LGB. The Disneyland Resort Express is about 50% more from LAX I believe (can't remember the exact amount at the moment). Shuttles and such are going to also be more from LAX, as it's further away from Disneyland.
I have a hard time recommending basic shuttle services; this is based purely on a safety standpoint. They are more top-heavy, and more likely to tip over... LA driving is rough, and a simple swerve to avoid a car accident can result in a tip. But, I know I'm admittedly more concerned about this possibility than most people; years ago, there was a wreck in my hometown, with a family on the way to the airport, and the father died in a shuttle van, and that really stuck in my head! This only pertains to the shuttle busses that are like the vans on a high truck chassis; the ones similar to what city transportation uses don't seem to be so likely to tip.
Edited to add: Whoops! Just re-read your post, and see that you mentioned SNA as your airport of choice! I'd recommend the Disneyland Resort Express or a hired car (limo, shuttle, whatever). It's a bit of a hike to get from baggage claim over to ground transportation at SNA, but it's doable with 6 adults and 3 kids.