Comfy walking shoes & water !
I usually start (or finish) at the Colosseum, then... Palantine, Forum, Trinity College Pub for lunch, Trevi Fountain, Spanish Steps, Pantheon, Piazza Navona... St Peters, then mooch around a few churches... if I have time. (Can be done in reverse)
Sistine Chapel, and Vatican Museum are good, but take up a lot of time, unless you are there before the queues.
So much to do, in so little time
Edit: I've done it a few times now, so don't hang about too long in each place. It might take longer the first time. (Nice cafes around the Pantheon).