Venice to Rome

Train. You can get direct trains (3hr 45min) that start right in Venice (S. Lucia stn) and end in the middle of Rome (Termini station) for as little as €39+ per person.

Flights take a little over an hour, but first you have to get out to the airport, then you have to get from the airport into Rome. So figure 4 hours minimum; probably more, at several times the cost once you've added in the vaporetto and bus or water taxi, and the train from FCO.

The train is indeed the sensible way. Buy your tickets well in advance (2 to 3 months) to get considerable discount. Trainline is a reputable agent which sells them at the same price as the rail companies (Trenitalia and Italo).