Direct Train From FCO Aeroporto to Florence Santa Maria Novella

There is only one station at FCO and you'll find it following the yellow "TRAIN" signs.

I wouldn't run the risk of buying in advance; trains rarely sell out, whereas top fare tickets (called BASE on trenitalia.com) are worthless one hour after the departure of the booked train. Discounted tickets (Economy and SuperEconomy) are wasted one minute after the departure.

Note that train will call at Roma Termini at 11:40 and at Tiburtina at 11:58. The FL1 airport train to Tiburtina station costs 8 € per person, the same leg on the direct Frecciargento costs 19.5 €. Tourists' trains...

Dario is not totally right. The discounted tickets are actually garbage a few seconds before departure, when the train automatic doors close and you are not inside.

Below is the image of the inside of the Fiumicino station. There are only 3 tracks, so you won’t get lost. In the picture below on the right side is the Frecciargento you want, the one in the distance in the middle track is the Leonardo Express to Roma Termini station. The train on the left track is the Regionale to Roma Tiburtina station.
https://goo.gl/images/zgr81K

I've taken the 11:08 direct train from FCO to SMN. While there is the convenience factor, I've also changed trains at both Termini and Tiburtina and neither change is complicated. If you plan to purchase tickets upon arrival at the FCO train station, I'd suggest you buy tickets for the first available train and get to Florence earlier. With an option between changing trains at Termini or Tiburtina, I'd pick Termini. The Leonardo Express generally runs on time, but I've had experience with the regional train to Tiburtina arriving late, thus making for a very tight connection.

Thanks, everyone.