In response about distance from sights. You can not stay anyplace that is a less than 5 minute walk from every sight, just due to where things are...but that doesn't matter you will be going that way once or twice, what you want to avoid is having to go far just to walk, or for a meal.
I guess that is why I like the Trastevere. It is just a short walk over Ponte Sisto to the Campo di Fiori area, a bit further, but not far to Piazza Navona and the Pantheon, The Capitoline area is about the same distance the other way, through the Jewish Ghetto area. To help, the #8 Tram goes up Via Trastevere, over the river and into Largo Argentina, from there, buses to Termini, Borghese, and the Coliseum. Along the river runs Bus #23, handy for the Vatican area; however we have walked to all, except the Borghese area, from the Trastevere.
What we do love is spending evenings and mornings in the Trastevere, lots of restaurants, nice bars and enotecas, you can also choose to hit the more crowded popular area, full of tourists, students, and locals...or go a few blocks the other way and spend your time with locals and families.