High speed trains from Rome to Florence one day, Florence to Venice the next day.

The 1hr15mins would approximately be the taxi time alone from FCO to Termini. I would stay in Rome on your first night.

Theoretically it's possible but I wouldn't count on it. Plan for possible delay of incoming flight, delays at immigration (customs shouldn't be anything but a 'walk through'), and timing of the train from FCO to Termini (which may be faster than taxi). I definitely wouldn't buy a non-refundable train ticket in advance for a 12:00 train, maybe for 2:00. It's about 1-1/2 hrs from Termini to Florence on the high-speed train.

Karen,

Transit through FCO may be a bit slower than normal due a fire there several weeks ago. I haven't seen any recent updates so not sure what the situation is like at the moment.

It's certainly possible to travel from the airport to Florence on your day of arrival, as the trip from Rome is only 90 minutes. In fact there's a direct train leaving at 11:08, but not likely you'll be able to connect with that one. You may be able to connect with a departure at 11:57, arriving Firenze S.M. Novella at 14:22 (time 2H:25M, one change at Roma Tiburtina). That solution appears to use the FM1 rather than the Leonardo Express, so be sure you board the correct train. You won't be going to Roma Termini with that one.

You can buy your tickets at the FCO rail station, either from a Kiosk or staffed ticket office. BE SURE to validate your ticket for the first train prior to boarding, as it's a Regionale. Failure to do so many result in hefty fines, which will be collected on the spot! Don't pre-purchase rail tickets, due to the uncertainties with your time frame.

If you miss the 11:57 departure, there's another one at 12:27. It may be possible to work out a slightly faster route using Freccia or Italo from Termini or Tiburtina, but I'd have to spend some time looking at it.

I think your assumption that your plane will land on time may be assuming too much. There is more to it than just the time spent in passport control and waiting for your bags to come off the belt, especially in light of the recent fire at the terminal, just get to Termini ASAP and buy tickets for the next fast train to Florence, they go every half hour. There is only a 4 euro price difference between Base and Economy.

This has been an enormous help! I was right in thinking there are so many different options FCO>Florence by train, and hard to figure out from different schedules/lines. I was worried that the trains could be sold out if we wait until the day, but I've certainly been on a few late arriving flights In the past. So there are direct trains from FCO through Tiburtina? I guess 2.25 hrs is pretty good if we can catch one. We plan a Segway tour at 8 pm in Florence, so just need to get in a few hours before that.

I always have to go straight to Florence and always go straight upon arrival when I land in Rome.
Just buy the tickets at the FCO station whenever you get to it (depending on flight delays or bag claim wait). You will likely have to change at Termini since there are only two direct trains a day from the airport ( at 11:08 and 15:08). All you need is about 20 min of layover at termini to walk to the high speed to Florence. There is a high speed to Florence every 15 to 30 min therefore the chance of a sold out train is virtually nil. At most you have to wait 20 min for the next one. Believe me I've done this countless times.