Most Rome guidebooks advise to take the non-stop, "express" train from Fiumicino airport to Rome's Termini station, which is known as the Leonardo Express.  This is a good idea if your hotel is: 1) near Termini station, or 2) on the "A" or "B" Metro lines. This train only leaves every 30 minutes, but tends to be very crowded and can thus be a bit stressful -  a one way ticket costs 14 Euro and it's only 1st class service.  A better option may be "Take Taxi".  For a family of 6 it will cost you 60 Euro.  They wait for you right at the airport (Your name on a sign held high) and take you to your hotel doorsteps.  Very reliable and comfortable.

If your hotel is along the "B" Metro line, then you might instead consider taking a regional, non-express train from Fiumicino airport to Ostiense (nearby there's another, useful station - the Roma-Lido railway terminus - which allows you to connect with the suburban trains to Ostia) or Tiburtina stations (which is also convenient if you need to take a bus to a nearby town, as the bus station is just outside this train station).  Regional trains from the airport come more frequently (every 15 minutes) and, although they stop at all stations,  they are not much slower than the "express" train - for example, the Leonardo Express takes 31 minutes to Termini station, whereas the regional train takes 30 minutes to Ostiense station, 45 minutes to the Tiburtina station.   A one way ticket on these trains costs 8.00 euro.

Find out the schedules for both lines on the Trenitalia website  (enter 'Fiumicino Aeroporto' as point of origin).