We love to fly JetBlue into Long Beach. JetBlue has tv's in the headrest of every seat and they take a standard headphone/earbuds. We bring headphones for our kids and they end up watching cartoons on our flight (it's only 1.5 hours). They used to offer snacks, for free, but I haven't flown with them in a year and a half so don't know if they still offer this.
Long Beach is TINY - it reminds me of schools that have too many students and put up some sort of portable classroom on the playground. The buildings at Long Beach remind me of the portables.

There are 4 (maybe 5) gates, I think, and you actually board and deplane onto the tarmac. You have to climb the portable stairs to get into the plane. We have gate checked our stroller before - if that is something you might be doing.
There are NOT a lot of food choices at LGB, so you might want to make sure you have food before you leave or pick up something on the way to the airport.
It took us 1/2 hour to get from LGB to DLR on surface streets when we flew in last time. I think we took Ball Road all the way. There are grocery stores along that route. We ended up stopping to pick up some water bottles and snacks.
There are car rental places directly across a small 2 lane street if you want to rent a car. There are shuttles available - but we've never used them since the prices always seemed so high compared to John Wayne. It was always cheaper to rent a car than to pay shuttle prices.