The port opens at 10:30am, boarding almost always begins before 1:00pm, usually at around 12:15. They will give you information on when and where to make various reservations. I would recommend arriving about 15 minutes before the appointed time, as they almost always begin early. Recently, they have been taking reservations as soon as boarding begins. I'd say make Palo reservations first, then the spa.
There's a buffet lunch served at both Parrot Cay and at the buffet restaurant (Beach Blanket/Topsiders). I prefer the buffet on deck 9, as you can grab your food and sit outside (assuming it's a nice day).
As to what to bring in a carry-on, if you'd like to hit the pools or one of the hot tubs, pack a bathing suit. You should be able to get into your room by 1:00pm or so. They will usually announce when the rooms will be ready. You can also go to your room to check to see if it's ready before this time. If the host or hostess is still working on, they'll let you drop off your carry-ons, if you like.
I believe the lifeboat muster drill begins at 4:00pm. All of the ship's services (bars, etc.) shut down at 3:30 and remain closed until the drill is completed.