Is there a direct train from the Rome airport to Florence or does one need to cab to another train station for that direct train?
No. Take the express train from the airport to Termini station, where you will get on the train to Florence.
Can I take a cab from the airport to the Termini station?
There's no reason you can't take a cab from the Airport to Termini, but why bother? You just have to switch platforms at Termini instead of negotiating the curb in front of the station. The train is 14 Euro while cab will be 42-46 Euro, and if there is traffic, the train will beat you there, its a tie if there if there is no traffic. Train leaves every half hour.
There is a fixed rate for taxis going between FCO and anywhere in Rome within the Aurelian Walls (which includes Termini). The current rate is €48. Take the Leonardo Express. The ride takes 32 minutes. Or to save even more money, but with a longer ride, take a shuttle bus which stops outside Termini.
There is a jumble of ticket stands at the Rome airport train station, many promising to sell both train and shuttle van transportation to Termini. The agent at the one I went to, with the shortest line, pitched me on a van, which was about the same length of trip and price as the train. Take your pick.
joe, There is no direct train from FCO to Florence, so you'll have to make one change. Here are a couple of options you can consider..... (1.) Leonardo Express from FCO to Roma Termini (trip 32 minutes, €14 PP - DON'T forget to validate your ticket prior to boarding the train). As I recall, the LE will be on the middle track. At Termini transfer to the next Freccia high speed train (300 kmH) heading for Florence (trip 1H:31M, Base standard fare €43, compulsory reserved seating, be sure to board ONLY the train specified on your ticket). You can buy tickets for both rail journeys at the airport rail station. Have a look at the www.roninrome.com website for details and photos. (2.) FM1 train from FCO to Roma Tiburtina station. From there transfer to the next Italo high speed train departure to Florence. You can buy your ticket for the FM1 train at the airport (DON'T forget to validate), but not sure if there's a ticket outlet at FCO for Italo trains, so you may have to buy a ticket when you arrive at Tiburtina? Travel time with Italo will be about the same as with the Freccia train. Note that in either case your destination station will be Firenze S.M. Novella. In the same situation, I'd use Option (1) as it's the simplest and easiest solution when tired and jet lagged. Happy travels!
In your case, since you are going to the Termini station anyway to take the high speed train to Florence, the Leonardo Express from the airport is the best option. I see no advantage of taking the taxi to go to the same place. The taxi will have to battle the traffic and costs 48 euro, instead of 14 euro for the Leonardo Express, which will get there in 32 min. regardless of the traffic. By the way the taxi will have zero chance to make that run from the airport to the Termini station in just 32 minutes like the train during the day, maybe at night before 6 am, but later in the morning with the commuters driving into the city it's impossible. Also the taxi will leave you on the curb in front of the station, and you still have to carry your own luggage inside the station to the platform where your train will depart from.