Watch out for train strikes. We were planning to take the train from Livorno to Pisa with a stop at Lucca, but they annouced a train strike so we ended up booking a shore excusion to Pisa instead.
We did take the train from Rome to Venice it took about 5 hours. But it was a nice comfy Eurostar train and we stayed two days in Venice. I wish we would have stayed there longer both my hubby and I loved Venice. Train system was very easy to use.