FCO to Cinque Terre

That will work. But it could happen since you are not buying in advance that the train will sell where you can't sit together

To begin with, yes, you can buy your tickets at the FCO rail station either from a Kiosk or a staffed ticket office. Once you arrive at the rail station, you'll see the options.

What time is your flight scheduled to arrive? There are a variety of train options available, and which one you'll be using will depend on which train you connect with. Here are some of the possibilities.....

• Departure from FCO at 11:08, arriving Vernazza at 16:13 - Frecciargento to Termini, Frecciabianca to La Spezia Centrale and Regionale to Vernazza. Your seats for the first two trains will include compulsory seat reservations, which will be provided with the tickets. Before boarding the train for the last segment, you must validate the tickets prior to boarding the train.
• Departure from FCO at 13:08, arriving Vernazza at 18:03 - Leonardo Express to Roma Termini, Frecciabianca to La Spezia Centrale and Regionale to Vernazza. Again, compulsory seat reservations on the Frecciabianca and the other two tickets must be validated before boarding the trains. NOTE that there are two trains serving the airport, the Leonardo Express and the FM/FR1. If both are in the station at the time, be sure you board the correct train!

There are numerous other solutions. Check the Trenitalia website for details.

Thanks for your help. Our plane arrives at FCO at 7:55am I am planning to buy our other train tickets (Vernazza to Lucca and Lucca to Rome) online as soon as I can to get the best price. I didn't think about the possibility of not getting seats together on the trains to Vernazza. Would it make sense to buy more expensive online tickets from FCO to Vernazza that are changeable in the event we miss our train? I am probably overthinking this and fretting too much!

The Rome to La Spezia leg is where you might not get the seats together if you buy on same day.
The 2nd leg is a piece a cake.

Buy the tickets in advance that allow you a credit or to change in case you don't make the train.
The cheaper tickets don't allow this. But considering that you are arriving at 8 am I would take the low risk gamble of buying the cheapest ticket online on the day you leave from the US on the fast train leaving from Termini to La Spezia after 1 pm.

That will allow you time to get oriented eat something find the right platform. Termini can be an sensory overload. And I missed a train the last time I was there in January by underestimating the distance of the platform; but it was just one where I could take the next one without having to buy a ticket.

Hi Bruce. For Vernazza to Lucca, do not buy online; there is no discount to buy in advance and you would unnecessarily restrict your timing. Just buy at the station in Vernazza. 11 Euro per person. Enjoy your trip!

"Would it make sense to buy more expensive online tickets from FCO to Vernazza that are changeable in the event we miss our train?"

In a word, No! In the event you missed the train you booked, changing tickets would probably involve standing in a long queue (and wasting time) while tired and jet lagged. That's not my idea of a "fun" holiday, and something I would try to avoid. I'd suggest simply buying tickets when you arrive at the FCO rail station on the next train heading towards Vernazza. Be sure to note which types of trains you'll be using, as you'll need to know which ones to validate tickets.

"I didn't think about the possibility of not getting seats together on the trains to Vernazza."

I wouldn't be overly concerned about the possibility of getting seats together. In all likelihood you will be able to get seats together. If you find that's not the case, you may be able to get seats across the aisle or nearby. You could also buy first class seats as it's not likely you'll have a problem there. One thing to keep in mind is that getting seats together will only be a concern on the express trains which have compulsory seat reservations. On the Regionale trains, there are no seat reservations so you'll just take whichever seats are unoccupied (or stand for a short time until a seat becomes available).

After a long international flight, my main priority is to get to my destination as quickly as possible so I'm not concerned about minor inconveniences.

Thanks for the info on your flight arrival time. I'd recommend not focusing on taking trains only from Roma Termini as that will restrict your options. There's a possibility that you may be able to connect with a departure from FCO at 09:12, arriving Vernazza at 14:33. That one has changes at Roma Ostiense and La Spezia Centrale. The middle segment is via Intercity, so that's the only one you'd have to worry about seats together (and you likely won't have a problem with that). NOTE that the first segment from FCO to Roma Ostiense will use the FM/FR-1, so don't board the Leonardo Express by mistake!

The next train after that is the 11:08 departure that I mentioned above. There's no way to predict how long it will take you to deplane, collect luggage, get through Passport control and get to the rail station, so you'll just have to "play it by ear".

" I am planning to buy our other train tickets (Vernazza to Lucca and Lucca to Rome) online as soon as I can to get the best price."

As Bob mentioned above, there's no big advantage to buying tickets in advance for the trip from Vernazza to Lucca. There are often two changes on that trip and you'll be using mostly Regionale trains. The price is always the same on those, whether tickets are purchased in advance or not. Some solutions do use an Intercity or other premium train, however the routes are short so you likely wouldn't save much money with advance purchase.

Be sure that you know the composition of the trains you'll be using on that trip, as you must validate locally purchased Regionale tickets prior to boarding the train on the day of travel or risk hefty fines.

For the trip from Lucca to Rome, you'll generally use a Regionale train from Lucca to either Pisa Centrale or Firenze SM Novella, and a Freccia from there to Rome. Again, Regionale prices will be same whether you buy in advance or buy on the spot. Be sure to note which stations you'll be using, as most cities have more than one. If you're willing to commit to a specific time, date and departure time, you can save some money by purchasing tickets for the Pisa / Florence train to Roma Termini. For example, on the Florence - Rome trip, Economy tickets are €34.90 PP and Base fare is €47 PP (they didn't have Super Economy listed). Those prices will include the compulsory seat reservations.

Thanks to all for your help!