Train from FCO to Florence

The only direct train FCO to Florence is at 1:53. You shouldn't have to wait that long, unless your flight is really delayed.
There are multiple trains from Termini all day long.

I'd wait til landing (and getting luggage- if you have ) then book whichever train you can make from Termini.
We just flew into Rome last month and were out of the airport in less than an hour- and we did have checked bags.

Take the Leonardo Express to Termini or take a cab- you'll need a taxi van for 4- it's flat rate 50 euros.
Go outside to official taxi stand and wait your turn- super easy, about a 40 min trip- so give yourself a bit of leeway so you can find your track at Termini and walk to it.

Get the Trenitalia and Italotreno apps now and use to book as soon as you arrive.
It's too late for any discounted tickets now anyway.

I would book asap. Give yourself a couple of hours after you land so you’re not stressed. Trains from FCO to Florence are pretty frequent and most if not all will change at Termini so I wouldn’t mess with a cab. Travel time is about 2.5 hours. I like trainline.com to book and see all the options in one place.

I like trainline.com to book and see all the options in one place.

I don't think trainline gives you all the options

Use the actual train sites
https://www.trenitalia.com/content/tcom/en.html
https://www.italotreno.it/en

I believe Leonardo Express is 18 euros/person now- so a taxi is cheaper. No tip needed.

Get the Trenitalia app, tickets after retrieving your luggage. Booking in advance is a mistake—adding enough slop you end up on a later train.

We just did this a few weeks ago - landed in FCO on May 25 and went immediately to Florence.

I booked our tickets from Rome Termini to Florence SMN about a month in advance on Trenitalia.com. I knew that I wanted to take the high-speed train, meaning that reservations are required, and the best/cheapest fare classes usually sell out in advance. Our plane was supposed to land in FCO at 7:45am, so I booked a 12:30 train from Termini to SMN to give us plenty of time.

It ended up being too much time, as our plane landed earlier than scheduled, and we were through customs and on the 8:30 Leonardo Express train, meaning we arrived into Termini at 9am. (Our customs experience was abnormally quick, though - I'm traveling with my 5 year old kiddo, and we were pulled out of the general customs line and sent to a "priority" queue that was actually for diplomatic passports. Sometimes traveling with a child has its perks! I digress, however.) Our tickets were changeable, but both the earlier trains from Termini to SMN were sold out. If we hadn't purchased tickets in advance, I'm not sure we would have made it to Florence that day, and certainly not with a seat on the train. That's a really long story for me to say - I'd definitely recommend buying in advance. I'd rather have a few extra hours to kill in Termini rather than not being able to find a train at all.

Wanted to let folks know about our experience. Flight landed at FCO at 8:30am. We were out by 9:30am and caught a taxi to Rome Termini. It showed arrival time of 10:00am. While in the taxi, I booked the 10:35am Trenitalia to Firenze SM. There were enough seats in most trains but if 4 of us wanted to sit together, then there were very few options left. We were in Florence by noon!

There were enough seats in most trains but if 4 of us wanted to sit together,

How could you say that? Trenitalia doesn't show the seat chart unless you check the "choose your seat option" and you would have been put in the same car even if you did not choose your sits. Once you are in the same car you can ask to switch, if you really need to stay close after 12 hours on a plane!

Anyway I doubt you couldn't find 4 close seats in business class, either.

I'm not sure we would have made it to Florence that day, and certainly not with a seat on the train. T

No, you would have take an Italotreno high speed train departing in a couple of hours with reserved seats.