The port does not open until 10:30am, so getting there much earlier than that is probably not worth your while. Boarding generally begins at about 12:15pm, but could be later depending on many factors, mostly on when the ship arrived that morning and how long it took to clear Customs and Immigration.
I believe that you can check your luggage when the port opens, but not before.
Your luggage may be in your room when you board, but likely will not. It has been once for us in four cruises. I'd pack a bathing suit in your carry-on if you want to use the pools or hot tubs on the first day. The luggage should be in your room by early afternoon, but on occasion, it isn't there by early dinner. The rooms themselves are not always ready when boarding begins. They usually tell you that they'll be ready at a given time, say 1:30pm, and direct you to the buffets for lunch.
What I'd recommend doing after you get on the ship is to hit the lunch buffet. It will be both in Parrot Cay and at the buffet (Topsiders/Beach Blanket) on deck 9. I like deck 9 because you can eat outside. If you're among the first to board, you'll have time for lunch before the "reservations scramble". If you want to book Palo, the Spa, or Flouder's Reef, you'll want to get to these places fifteen minutes or so before they begin taking reservations. If you're boarding early, you should have plenty of time for lunch before having to do this.
