For the very best landmarks, like the Colosseum, it's a great idea to pay for a tour. While it might cost a little more than the regular entry price, you'll often be able to skip the line and will get much more insight into the place you're seeing.
If you'd prefer to skip organized tours, it still makes sense to book your regular entry tickets ahead of time. Typically, this will allow you to head straight into the attraction. This includes the Vatican Museums and the Colosseum, for example. The Vatican City itself, including St Peter's Basilica, is free to enter, but there's often quite a queue, and so arriving early is a good idea.
Rome is a large city with plenty of traffic, though the public buses are still a great transportation option. See if your destination is near a metro station, as the system is easy to understand: Fittingly for the home of Catholicism, it's arranged in a cross formation. Many of the best sights, including the Colosseum, Roman Forum, and Circus Maximus are right near each other and easy to walk to.