Welcome to the world of cruising. For a first cruise you picked a great family ship. I am guessing you did a lot of research and/or got the advice of a good travel agent.
Independence is one of the premier Royal caribbean ships of the Freedom-class. It has all kinds of fun features your kids especially will enjoy; flo-riders, a water park, mini-golf, video arcade.
You will like the entertainment and the parades and pubs in the Royal Promenade. To find people on the same cruise, go to our "meet on board" section in the forums under "Royal Caribbean"