Train Travel From Terni to Ostia Antica

Hi. I am traveling in Italy in the first week of June. On June 6th I need to get from the Terni train station to an Ostia Antica AirBnB (really close to the Fiumicino Airport). One route is taking me by train from Terni to the Rome Temini then by train to the Airport then by Uber or bus to the AirBnB. Another route is taking me by train to Roma Tiburtina then by train to Parco Leonardo then by Uber or bus to the AirBnB. Which would make more sense? Does either option offer a fancy or more fun train? This will be my kids first time on a train and I am willing to splurge if there is a faster or cooler option. I obviously don't really know what I am doing, so any advice is welcome.