There are two operators on this route, "Trenitalia", the national operator, and "Italo", the competition.
They both run on the same tracks at the same speed, and compete on price and comfort levels.
They both offer at least one train per hour, so the answer to the "convenient" question is when do you want to travel?
The "safe" question is one people from North America seem pre-programmed to ask, What do you mean by safe? Train is a lot safer than road, and at 200 MPH you don't get people wearing masks standing on the tracks holding up trains.
The main station in Rome is "Roma Termini" and in Florence "Firenze Santa Maria Novella, often abbreviated to Firenze SMN.
I would also expect it to be cheaper to book direct with Trenitalia or Italo than going through a travel agent.
For more info about trains from Rome see here: http://seat61.com/international-trains/trains-from-Rome.htm