Venice, Florence, Lucca, Cinque Terra, Rome

Your choice would be Venice to CT, then CT to Florence, then Florence to Rome. Do Lucca as a day trip from Florence.

OR

Venice to Florence (do Lucca as a day trip from Florence), then Florence to CT, then CT to Rome.

Total time on trains for these 3 legs won't be much different between these choices.

Is it possible to do a loop of some sort. It seams like extra travel to go florence to lucca to florence to cinque terra no?

You could do either Venice to Florence to Lucca to Cinque Terre to Rome, or

Venice to Cinque Terre (via Milan and Genoa, down the coast) to Lucca to Florence to Rome.

No backtracking either way. The first one has shorter travel time on the day leaving Venice, then longer on the day leaving Cinque Terre going to Rome. The second gives you a longer but more scenic day on the trip from Venice to Cinque Terre via the coast.

That is, with the first route, Venice to Florence is 2 hours; La Spezia (for Cinque Terre) to Rome is 4.5 to 5.5 hours.

With the second, Venice to Monterosso (for Cinque Terre) is 5.5 hours (single change in Milan), then Florence to Rome is 1.5 hours.

Venice 4N > Florence 4N > Lucca 1N
Cinque Terre 2N > Rome 3N.

Or do 3 Florence and 2 Lucca.

Thank you for weighing in and for your advice. If I am understanding correctly, I should go Venice to Cinque Terra to Lucca to Florence to Rome s it is the most scenic or was it Venice, Florence, Lucca, Cinque Terra to Rome in terms of scenery? It wasn't as clear which to do.

Also, should we train this whole thing or is it best to rent a car at some point. There are 4 of us so I am trying to weigh the economics with the convenience.

Finally, if the trains from Venice to Cinque Terra have stops do we have to switch trains?

Thank you all.