You will be amazed at how much storage space there is in the cabin. There will be plenty of drawer space and closets to accommodate a family of 4. Unless you are a REAL over packer and pack 10 days worth of clothes for a 5 day cruise.
The one area that may be lacking on space is the bathroom. A hanging toiletry bag or "over the door" shoe holder works great for keeping all the toiletries together.
You can store your luggage under the beds. Just slide it under the bed. You may need to lift up the bed an inch to get the suitcase under the frame.