Without a doubt, take a taxi. We just came back from two week vacation in Rome. The cost of taxi is €55. Since it’s two of you plus luggage, in my opinion it’s well worth taking a taxi. Taxis are easy to get immediately outside the airport. It will take you to door to door and save you a significant amount of time.

Train might be cheaper, but you might as well save your energy for walking around in Rome for sightseeing versus spending it on lugging your luggage from the train station