There are two issues here:
-- When the port area opens
-- How you check your luggage
If you arrive at 10:00 a.m., you probably won't even be allowed into the
DCL terminal area.
Once they open up (around 10:30 a.m. or so), you will be directed to a spot where you can check your baggage. Don't check any baggage containing liquids or anything that could be considered a weapon. As when flying, you should carry on valuables, medications, cameras and film. Also, make sure you carry on anything you'll want to have the first afternoon, such as swimwear.
The folks who take your baggage depend on tips. Plan on $1 to $2 per bag. For a family with 6 or 7 bags, a $10 bill works well.
You now have only your carry-on items. You'll go into the terminal, passing through security at the entrance. The first passengers are allowed to board the ship some time before noon.
Your luggage will show up in your stateroom any time between 1:00 p.m. and 5:00 p.m. You don't need to tip the stateroom host/hostess when he/she delivers your baggage. (You'll tip the stateroom host/hostess at the end of the week.)