Personally, I would not book a flt out of TIA before noon at the very earliest. We have cruised out of Tampa twice. The first time we did the traditional debark and did not arrive to TIA until 10:45, but we had a 2pm flt so all was good there. Our last cruise, we got a good deal on and 11:35 am flight and made it doing self-assist debark, but anything earlier than that is really going to be a dice roll.
As far as hotels, we use the ones on Rocky Point near the airport because thay have a great cruise pkg: free airport shuttle, free breakfast, and a round trip shuttle to the port and then back to either TIA or the hotel for those that booked the park and cruise.
Here are the names of the three and I would go with any one of them depending on the best rate. We ended up at the Holiday Inn both times but it just happend that that was the best rate at the time.
Holdiay Inn Rocky Point, Hampton Inn Rocky Point and Chase Suites Rocky Point. All three hotels are right next to each other. They all overlook the Bay and have a Bahama Breeze restaurant in the adjoining parking lot areas.
The Westshore area and Tampa Airport area are some other areas to check as well. Downtown Tampa hotels will put you closer to the port but very few, if any, have airport shttles and their rates are much higher.