SNA/John Wayne is my favorite. It is the closest to the parks (about 15 miles) and is a great smaller airport. Next up is Long Beach, maybe 20 miles away and it is a really small but very efficient airport. These 2 are always my first two choices, even if a connection is needed to get there. Third choice for me is Ontario, then Burbank, and lastly the beast that is LAX. It can take you 1 hour to get to/from LAX, or is can take 3. That’s too much lost time for me, so I usually stick to close by. There is no need for a car at DLR. We just take Lyft, not sure if there are any shuttles anymore since Supershuttle went out of business.
No idea about strollers. There are ECVs for rent outside the gates, but if you want one for getting to and from the hotels, there are some places on Harbor that rent them. Will you stay onsite?