Hi Laura,
I'm not Sky, but we sail out of Tampa almost every year. So much easier for us than other Florida ports. The parking lot is across the street from the pier, but it is not free for long term parking. They also offer valet parking, but it is so close, we never saw the point to this. You can pull up, drop off the luggage, including carry-ons and leave one person to watch over it. Then, swing around and park. Very easy.
The check-in for Carnival is very well organized and moves faster and easier than any other port we've sailed from. We usually get there around 11 a.m. to maximize time on board. If you are flying in, have you considered using a shuttle? As far as Carnival being a good choice, I would say yes. In spite of some other peoples' opinions, I have always enjoyed Carnival. And I love the size of the ships they have out of Tampa. I don't like the huge mega ships and the Skyway Bridge limits the cruise lines to the somewhat smaller ships.
JMHO
Marty