Frank's tips are also awesome. Yes yes, do NOT bother renting a car for Rome. Eek! You're familiar with those teeny tiny Smart cars, yes? A lot of people in Rome drive those because the alleyways are so narrow and crooked, and there is no parking for full-sized cars. People park their Smarts like Americans park their bicycles. You don't want to have to worry about that. Plus, it's VERY easy to get around by bus, train, or walking.
Ooooo I just went to check Rick Steves' website, and I forgot he has a great little iPhone/Android app! I checked, and he has walking tours of the Colosseum, the Forum, the Jewish Ghetto, Ostia Antica (this requires a drive or bus ride to the outskirts of the city, but it's fascinating), the Pantheon, Pompeii, St. Peter's Basilica, the Sistine Chapel, and Trastevere. Looks like you could have Rick Steves as your persona guide!
I do agree though, signing up for a tour at the Vatican is probably worth the extra money. If nothing else, it lets you skip the humongous line just to get inside.