Hotel is short, covered walk to terminal. Agree that train into Rome is the best way. Note: it is not necessary to go to Termini. There are other stations served from FCO and you can catch a bus, tram or, sometimes, metro from these other stations. Depends on where you want to go in Central Rome. Termini is not the neatest of neighborhoods. Reminds me in some ways of the Plaka in Athens, or the area near the bazaar in Istanbul, or Brooklyn. Just be aware of your surroundings and you should be fine.
Hilton Rome Airport had a great buffet and welcome amenities when we stayed overnight prior to a flight. If you renting a car and are driving to another city, it has free (yes, free!) parking in front of the hotel between the hotel and the terminal. Autostrada access is easy eliminating the need to drive in Rome proper. There is little traffic near the airport so driving is easy.
Driving in Italian cities is an incomparable experience. Scariest one was Bolzano where five lanes of traffic on a two lane road approached us at high speed. second scarriest was Florence being stuck on a circle for 20 minutes in order to reach our hotel. Third was driving from Termini station out of Rome.
Yes, I have driven in Istanbul, Paris, London, Athens, Boston, Manhatten, and New Jersey. Italy is the scariest, but only on city streets.
Enjoy your Rome Airport, Hilton stay. Suggest you stay only one or two nights because it is a significant trip into central Rome.