Since we always drive, I'll leave the limo/bus to others.
We have always arrived about 10 or so, 10:30 is a good time, they have always just opened the building then. All of your luggage is taken first thing when you arrive, and will delivered to your stateroom. So take on anything valuable (cameras, medicine) and breakable in a small carry-on bag. We went from one carryon each the first time to one small one for all of us the last trip. You really don't need to cart much around waiting for your stateroom to be open at about 1:30!
When you get on, don't let them push you to eat inside, instead go topside where there is a buffet. Great food, great views, and you're either looking out a picture window or you can sit outside on a good day.
I think the best thing for the 4 & 8 year old is to swim! Just take a change, find a bathroom, and the kids pool will be open and the least crowded of the whole trip. A great slide, and a great time.
Explore the ship. Go to your stateroom when they open. Make reservations as you might want them (Palos?). Then DO NOT miss the sail away party. Watch the other cruise ships pulling out and feel sorry for them that they aren't on a Disney ship!