We did a transaltantic from Miami to Rome. I would suggest doing Rome to Miami you will be rested on the trip back. Plus you will gain time back on the trip to Miami. The train system in Italy is very good. After our cruise finished in Rome we took a train from Termini station (Rome) to Santa Lucia station (Venice) it was very easy to book and super comfortable. You want a Euro Star (ES) train they are very fast. You can also take the train to Florence if you want.
This is the train website. I could not get it to work to buy tickets so I just got the tickets once I was in Rome. But it has good information about tickets. I got a 2nd class Standard Fare ticket. I hope that helps.
Trenitalia - The ticket