That sounds like a good plan. Relative to ticket pre-purchase - I'd get the Trenitalia app and, if you're comfortable with it, use it to select and purchase tickets when you land. That way you don't have a flight delay or something that screws up your train.
Relative to picking up a rental car at the airport, it's not far to the airport but getting one in town isn't an issue. Read this -
https://www.visitflorence.com/touris...-ztl-zone.html - if you're still nervous about picking up in town the certainly take a cab to the airport.