Complete beginner... Which camera??? Which book???? ~*~Thanks!~*~

I am a complete beginner!  I have only used the simple point and shot, auto focus type cameras. I want to buy a camera with a couple of lenses and a really good book then learn how to use them (the hands on way~ I guess).

I have a budget of around $1,000 (to $1,500 if necessary) for a camera and lense kit.

I have 3 kids so I want to be able to take a variety of pictures. My daughter plays valleyball and basketball so I want something that can do action in a low light gym. My son runs cross country so I need to do distant action photos. I also have a newborn so I want to be able to take close ups of him doing his thing.

What camera (or cameras) would you suggest to get me started? I realize I will need to upgrade down the road.

Also, is there a book that is good for teaching a newbie like me??? (I know I can read stuff on internet but honestly I don't even know where to start. So, a book that goes chapter by chapter seems like a good way to start!)

Thank you so much for taking the time to read and answer this post! I really apprecite your willingness to help me.