We've done Carnival, Royal Caribbean, and Celebrity, and enjoyed all of them. I wouldn't worry too much about the specific line. Instead, focus on where you want to go and what dates seem to align the best (as well as budget considerations).
For a first cruise out of FL, your best options are a 7 night Eastern or Western Caribbean. Read up on the port stops and see which ones best suit your tastes. Since you said you're not into crazy onboard activities, I would choose an older ship. They tend to be smaller and less expensive, while still providing the same overall experience.
Do try the onboard shows, since they're included in the price of your ticket. I absolutely love them, but if you don't, nothing's making you stay
Also read the newsletter/calendar they put in your cabin each night, and try some of the onboard activities. Art auctions are fun even if you don't buy anything. There are generally different ship tours, classes in everything from napkin folding to ballroom dance, Bingo games, sometimes guest lectures...a big part of cruising is getting involved.
It's definitely easiest to book shore excursions through the cruise line. But if you're comfortable with travel in general, you'll pretty much always save money and have a better experience booking independently. For example, when we cruised Alaska, we bought the Great Alaska Toursaver for $99. It was packed with BOGO discounts for the very same tours offered through the ship. And they were all small group tours rather than the giant bus provided by the ship. Or in Grand Cayman, we made a car rental reservation ahead of time. Went the same places as the bus tour plus several others, all on our own schedule. Just something to think about.
