My preferred options.
If you can, pick Long Beach (LGB) instead, a nice small airport and old school. Luggage pickup is still outdoors under a roof. The drive is easy, the airport exit (and there is only one) places you onto Wardlow, which changes names to Ball Road in a few miles, take that to
Disneyland. No turns needed, just some traffic lights to deal with. And at 14 miles, the same distance as John Wayne/Orange County/Santa Ana (SNA) is between the airport and Disneyland.
As for driving to Disneyland, take the main freeway exit from John Wayne, and pick the 55 north option, as soon as possible get in the Carpool Lane (I presume 2 or more in the vehicle) and use the special carpool flyover to the 5 north, and exit at Disney Way, using the special carpool exit. Just make sure and stay on the I-5 instead of switching to the 57 - Right side option on the carpool lane).
On the way back, get to Gene Autry Way (Disney Way or Katella to Haster South, then left (east) on Gene Autry Way, take the special carpool lane onto 5 south, use the carpool flyover to the 55 south, take the 405 south carpool exit, and during the ramp, there will be a special John Wayne exit before you actually get onto the 405.
And recommend avoiding LAX, followed by Burbank/Bob Hope (BUR) and Ontario (ONT) as options unless you have no other option.