You can buy a BIRG ticket which will get you back and forth to Rome and all metros and buses in Rome for about 9 Euros. If there is a long line to buy tickets, there is a "Tabacchi" to your right when you walk into the train station and they sell the same tickets. Ask if the little children need to have tickets, and don't forget to stamp your ticket at the start of your journey. Trenitalia website will give you all the timetables. Remember that the San Pietro stop is right by the Vatican which might save you some time. Also Bus 64 runs by the Vatican and goes close to all the other sites of Rome.