Rome Italy - Train Help!!!?

Question

I need to get from the Colosseum to:

Port of Civitavecchia
Molo Vespucci
Civitavecchia, Italy 00053

The cheapest way is by train, correct?

Which trains Exactly do I need to take?
If at Termini Station, which train do I take to my port?
And will I be Right at the port and see my huge Cruise when I get off the train?

I will have to arrive on time to catch my ship at the port. Thank you!