We've been twice, and stayed once near Termini , and once near the Ponto Sisto bridge. If I was to go again without kids, I'd choose the second location as it was walking distance to Trastevere, which was a wonderful place to spend the evenings. With kids, I'd try to stay near to the Villa Borghese.
If you are staying near a metro or station, getting the Terrevision bus is easy and cheap. Or , depending which airport you land at, the train is easy and cheap - we got a train to Trastevere, then a tram.
If you want to visit the Vatican, book online before you go. It can save a long time queuing.
Besides all the usual tourist sites, if you get time, take a walk through the Rose Garden to the Piazza of the Knights of Malta, and peek through the keyhole of the gate there for an amazing view of St Peters.
Be prepared to walk a lot - it's the best way to get around. Take comfortable walking shoes/trainers. Just wander and see what you come across, we found so many beautiful churches, little shops etc
Have a great time - Rome is a beautiful city.