We will have luggage and need to get from Rome Termini to the cruise port at Civv on a Sunday
Take the train. When you reach the end station, simply grab a cab to the port.
https://www.trenitalia.com/en.html
You can buy tickets from the machines in the station or on an app on your phone.
Here is a link to a you tube video that covers this in detail.
https://www.youtube.com/watch?v=nir9eRb8ZDQ
Many people simply take the train and then a taxi to the port entrance. However, if you have a lot of luggage, you might consider a private car service. If will be somewhat expensive, but not when compared to the total cost of the cruise. We've used Rome Cabs (a real car service despite the name) a number of times to and from the airport and have always been happy with the service. They also take folks to the cruise port. Just google them, send an email detailing your needs, and you should get a reply within 24 hours. If they can't take care of you, perhaps they can suggest another car service. We'ed not hesitate to follow their suggestion.
I think the cost of a private car transfer from Rome to Civitavecchia is 120€ for up to 3 passengers. The trip is less than one hour mostly on freeway.
The cheaper alternative is a train that can take you there in just over one hour for less than 5 euro per person. The Civitavecchia station is a long walk from the port, so once there you should take a taxi for the last mile. Be aware that lots of Cruiseders travel there by train, so the wait for the taxi may at times be longer than expected.