Rome to Venice

What to you mean or are asking about "best train."? For some the fast train is best even thought it is the most expensive. Others will use a slower train to save some money. For us, the best train is the one best fits our schedule. It is your personal preference. Or what is important to you.

Penny, My suggestion would be to use the EuroStar Italia / Alta Velocita (FrecciaArgento) trains. There are numerous departures, even on a Sunday morning. For example, if you chose a departure of 09:45 from Roma Termini, you'd arrive at Venezia Santa Lucia at 13:33 (time 3H:48M, current second class base fare of 76€). Check the Trenitalia website as you may be able to get a discounted "Mini" fare on that route. Keep in mind that with those fares, you'll be "locked into" a particular train and departure time. There are also cheaper trains available, but the travel time is about twice as long. Happy travels!