First time in Italy, in March. Need help!

You have just the right idea, head to Venice on arrival and work your way back to end in Rome. Or, if you think you will be just too tired on arrival, head to Florence first (shorter journey), then Venice, then Rome.
I think three stops in just under two weeks is perfect and I would save Cinque Terre because it is just so much time on the train and not ideal weather-wise. If you want a breather from the cities, I would pick somewhere in Tuscany aside from Florence.
https://www.discovertuscany.com/tourist-info/
https://www.visittuscany.com/en/index.html
You could also do day trips from Rome or Venice--pick what appeals to you the most. Enjoy!

Jadsjbd,

You are going to love Italy. Rome to Venice is no quick trip (7-8 hour train ride). Since its your first time in Italy, sometimes you need to adjust first before hitting the ground r=running. I would maybe think about this itinerary:

Days 1-4: Rome
Day 1:
Arrive in Rome, check out Pantheon, Trevi Fountain, and Spanish Steps.
Day 2:
Visit the Colosseum, Roman Forum, and Palatine Hill, followed by an evening in Trastevere.
Day 3:
Explore Vatican City, including St. Peter's Basilica and the Sistine Chapel.
Day 4:
Consider maybe a trip to Orvieto, or explore more of Rome if you prefer.
Days 5-7: Florence
Day 5:
Take a high-speed train to Florence (approx. 1.5 hours). Exploring the city center, including the Duomo and Ponte Vecchio.
Day 6:
Visit the Uffizi Gallery, see Michelangelo's David at the Accademia Gallery, and see the Boboli Gardens.
Day 7:
Consider a day trip to Tuscany, perhaps visiting Siena and San Gimignano
Days 8-11: Venice
Day 8: Take a high-speed train to Venice (approx. 2-3 hours). Exploring the city, perhaps starting with St. Mark's Square and the Doge's Palace.
Day 9 & 10: Enjoy a gondola ride, explore the canals, and visit St. Mark's Basilica.
Day 11: Take a vaporetto to the island of Murano, known for its glassblowing, or Burano, famous for its colorful houses.
Days 12-13: Return to Rome
Day 12:
Take a train from Venice to Bologna (approx. 1.5 hours).
Day 13:
Take a train from Bologna to Rome (approx. 4 hours). Arrive in Rome

Hope this helps.

Rome to Venice is a 4.5 hour fast train (not 7-8)

I would head to Florence on arrival 4 nights
Then train to Venice 4 nights
Then train to Rome-5 nights-take a picnic on the train, this will be a nice rest day

We did catch a train on our first day the last time we went, but I feel I should add a word of caution. With jet lag, we struggled to stay awake ( it was about a 2hour ride to Naples) and you don't really want to sleep through the travel. As well, we had been to Rome just a couple of years before, so knew where we were navigating etc. For my first trip to Italy, I think I would prefer to take it more cautiously. As well, you can get a good price on. a high speed train to Venice, but you don't want to risk losing that if your flight is delayed etc.
I would suggest picking two places in Rome to stay, that way you can explore different neighbourhoods on foot. Stay 2 nights in Rome when you get there, then catch the train to Venice, and work your way back. Cinque Terre is a long way from Venice, so pick one. A sample itinerary would be:
Rome 2 nights
Venice 4 nights
Florence 2 nights
Tuscan town ( maybe Siena as you can bus or train back to Rome) Or Lucca is close to Florence but farther to Rome)( Or Orvieto which is right on the train line to Rome) 2 nights
Rome 2 nights

I added in a smaller town, because I feel the charm of Italy is often in those towns. Orvieto is technically not Tuscan, it is in Umbria, but it is lovely and would be very different from what else you will see. I'd probably pick it for ease of travel

Rome to Venice is no quick trip (7-8 hour train ride).

That is not correct.
Trenitalia shows the travel time from Rome to Venice as 4h 34 minutes ( some departures show 4h 39 minutes).

I like your idea to press on to Venice on your arrival day vs splitting your time in Rome and adding the extra hotel transfer

No idea where on the planet you are. Was surprised that you said multi city was so much more than the r/t so I did a Seattle to Rome r/t comparison to a multi city Seattle to Venice/Rome to Seattle routing for mid March and the latter was cheaper than the r/t trip pricing..

Your trip would be so much more efficient if you could avoid having to back track to Rome to get home.

Another option is to buy a cheap ticket from FCO to Venice instead of taking the train. The train involves a connection in Rome which is never fun when hauling luggage.
How many nights will you sleep in IT? Venice deserves a minimum of three nights, the Cinque Terre two nights and if you hike add a night per hike. Florence alone needs three nights and Rome four nights.

Thank you for all the replies! There is so much to consider, and plans to make, and so don’t want to screw up big time!

We will be there for 13 nights total. I may look into a short flight to Venice. I hadn’t thought of that, only trains. It would be wonderful if we could find one that would get us there without too much hassle after traveling all night!

The drawback with a flight to Venice is that because it will be booked on a separate ticket, you'll need a large cushion of time between the flights, and that means hanging out in an airport for hours--not fun with jet lag! If you don't think you have the wherewithal to press on to Venice that day, just go straight to Florence--that is much more manageable on arrival (when you usually can't check in until afternoon anyway. Just store your bags in Florence or have the hotel hold them and have lunch and take a walk while waiting to check in. There may even be a train to Florence from the airport that does not require changing. Check schedules on the Trenitalia website but don't purchase in advance in case your flight is delayed.
I have napped on many a train with jet lag, and it was always fine! Hubs and I take turns napping, or I just loop my arm around my bag.

Be sure you are taking into account all the steps/time/cost of taking a flight to Venice from FCO.
You have to allow a buffer in case your flight is delayed so I wouldn’t book any flight less than 3 hours from your expected arrival. You have to go thru passport control on arrival, retrieve bags (if checked) then go back thru security to your next gate and check in there- check luggage again as well. Most airlines want you checked in 45-60 min preflight. 3 hours might even be a bit tight.
The flight is only 1 hour but then you have to get from VCE into Venice so allow another hour for bus/vaporetto/alilaguna boat or water taxi. That’s another expense.

If you plan to just take a train on arrival- Florence is the closest- there is usually just 1 direct train to Florence from FCO at 1:53- that’s a long time to hang around if your flight from US arrives early am.
Don’t book any onward travel train tickets- there are trains to Florence every 30 min or so- take the LE to Termini then next fast train. You can book that entire journey once you arrive at FCO- either at a kiosk or on the app. You will pay Base Price but no risk of losing money if you miss a prebooked train or flight
You would be in Florence much earlier than you could ever get to Venice- flight or train.

There is also nothing wrong with just splitting your Rome stay- 1 or 2 nights at beginning of trip, 3-4 nights at end. Stay in a different neighborhood and plan your sightseeing accordingly.

https://www.trenitalia.com/en.html
Station names:
Roma Termini
Firenze SM Novella
Venezia S Lucia

Good information about the time it takes and going through passport control and getting bags. I always over pack and check luggage, but am going to try to bring the bare minimum, knowing we will be dragging the luggage around every time we move on, so maybe I can finally manage just carry on. Knowing we can’t check in until afternoon, it makes sense to just get on a train and go to Florence or Venice. We’ll be exhausted either way, and at least we can sit down and take turns napping. We’ve never traveled outside the US, so don’t know what effect the overnight travel will,
have on us, and have never used our passports, so don’t know the drill. We do have business class lie flat seats, so hopefully we can get some sleep on the plane.

My wife and I went to Rome in March. We did it a little different by arriving in Rome first. We spent three days there before joining the 9 day RS Venice, Florence and Rome tour .
We fit in a bunch of sites in Rome that the RS tour doesn't go to because of the crowds.
We got tickets for the attic area in the Colosseum, the Scavi under St Peter's Basilica and Vatican tickets.
Then we took the fast 4hr train to Venice and joined the tour there.
I cannot say how much we enjoyed this tour. It was our first but not our last. If you don't want to join the tour watch the RS shows on Venice, Florence and Rome. It is a copy of the tour we took. Even down to the tour guides we had at the forum.
It was nice to get acclimated to the time change before traveling to Venice on the train. You also want to take the train because the station is steps away from the boats that take you into Venice.
The weather was nice by the way. Light jacket and no rain. At least until the last night.
Have fun