Trains from FCO to SMN Florence

There are a ton of options. I think the ItaliaRail site (https://www.italiarail.com) is the easiest to use.

Buy your ticket when you have cleared the immigration process.

Take you 'title' and put it in the Search box ( above) for numerous discussions on this topic

If you can clear all your arrival obligations in time, as arriving at 8am should provide you the opportunity, there is a Trenitalia frecce train that runs direct from FCO to Firenze SMN at 11:08 and 15:08.

No change of train needed.
I got lucky last year with a scheduled 10:40 arrival, which, given the extra "pad" time added to flight schedules and a friendly tail wind, got to Rome early. With a little dash to the train station within the airport, I was on my way to Florence on the 11:08.

Take the Leonardo Express to Termini and get the next train to SMN. You’ll be in Florence by about the time the 11:08 leaves FCO.

Do not use ItaliaRail as suggested above. That is a travel agency based in Massachusetts not the Italian Rail company. They do sell train tickets (at a higher price) but I’m not sure their timetable shows all trains, or only the ones they want to sell you.

The real train company website is:
http://www.trenitalia.com/tcom-en
Enter the following:
From: FIUMICINO AEROPORTO
To: FIRENZE S.M.NOVELLA
Date: enter the date of travel if in the next 3 months, otherwise use any date to see the timetable
Hour:08
You will see all available combination from 8am forward. There are two solutions per hour on average.
In most cases you may have to change trains at Roma Tiburtina or Roma Termini, but at 11:08 there is a direct Frecciargento departing from the airport which requires no changes (the train final destination is Venezia Santa Lucia).

If you buy ahead of time you can save with an economy or Supereconomy ticket, but it is risky to do so on the day of landing. If your plane is late and you miss the train booked, the discounted tickets are not changeable or refundable. If you don’t want to take the risk, buy a full fare ticket at the airport station at the ticket window or the automatic kiosk.

We took the 11:08 direct train from FCO with no change at Roma termini. Being tired, it was nice to not have to deal with a train change. We had espresso at the snack shop at the FCO train station while we waited for the train. It wasn’t fancy, but the coffee was fine and staff didn’t seem to mind that we hung out for awhile.