Florence Amerigo Vespucci Airport (Peretola): Take Tram T2, not a private transfer, to Firenze Santa Maria Novella (SMN): about 20 minutes end to end, generally every 5–15 minutes. Budget roughly €2 for a single urban ticket; older published fares are €1.70, so check the machine/app on arrival. A taxi is worthwhile only for a group, heavy luggage or a difficult address: the historic-centre flat fare has been about €25 plus luggage supplements.
Firenze Santa Maria Novella: This is the station you want. It is on the north edge of the old town, about 10–20 minutes on foot from most central hotels and sights. High-speed trains link Rome in about 90 minutes, Milan in about 1 hour 40 minutes, Venice in about 2 hours and Naples in roughly 2 hours 50 minutes.
Bologna Guglielmo Marconi Airport: For many European flight schedules this is the best alternative to FLR. Take the Marconi Express to Bologna Centrale, then a Frecciarossa/Italo high-speed train to SMN; allow about 1 hour 15 minutes to 1 hour 45 minutes airport-to-Florence once the connection is included, and roughly €30–50 total if booked sensibly. Do not buy an expensive direct car transfer unless your timing or group size makes it rational.
Pisa International Airport: Use the PisaMover to Pisa Centrale, then a regional train to SMN. Allow around 1 hour 30 minutes to 2 hours door to door, including the airport link and connection; budget roughly €15–20. It works, but Bologna is usually the stronger alternative-airport choice for Florence.
Rome Fiumicino Airport: For long-haul arrivals, take the Leonardo Express to Roma Termini, then a high-speed train to Firenze SMN. In a clean connection it is about 2 hours 45 minutes to 3 hours 30 minutes airport to station, and usually beats landing at Milan Malpensa for Florence. Leave a generous buffer: a missed Italian rail connection can wreck the plan.