Welcome to cruise-chat. When you arrive at the port there will be porters that will greet you to take your luggage (you should plan to tip them $1-$2 per bag). Make sure you have the luggage tags the cruise line gave you attached to your bags - BEFORE you hand it over. Now, you will want to plan to also bring a carry-on with all essentials to get you through the first day of the cruise (that you will bring on board yourself). I usually pack any meds, my toiletries and make-up, a bathing suit and a change of clothes. If I am traveling from somewhere warm and already have on shorts, I will pack a pair of casual slacks for dinner. When I travel from up north - I am usually wearing a pair of casual slacks and then I will pack a pair of shorts. When the porters take your luggage, it will be delivered to your cabin - but sometimes that is not until after dinner. (Not only do they have thousands of pieces of luggage to deliver - but it all goes through screening before it is brought on board and this takes time). While others are stressing over where there luggage is - you can relax and enjoy your first day onboard.
Tampa is a very nice port and close to the airport.