I am interested in their history and culture, but even moreso, I want to know how they lived: what they grew, how they grew it, how they cooked it, how they caught/hunted animals, what they lived in, what they slept in, what sort of social policies and issues did they have, how did they conduct warfare...
I'd recommend John Hann's Apalachee: Land Between the Rivers, Jerald T. Milanich's The Timucua, and Randolph J. Widmer's The Evolution of the Calusa: A Nonagricultural Chiefdom of the Southwest Florida Coast. Together these will give you a good introduction of the three main Contact-era cultures in Florida. And, of course, the Smithsonian's Handbook on the Southeast is a useful resource here too.
Conveniently, I have a post on these three societies already if you want to get a quick summary of them. If you have some follow-up questions, feel free to ask.