I was formulating an answer in my head...then saw Connies response and could not agree more, we did about the same. To just point out the pluses of her itinerary:
St Peters is open early, so you get an early start. Get the Vatican Museum out of the way as soon as it opens. HOWEVER, This does not work on most Wednesdays due to the Popes Audience.
The Spanish Steps are a natural starting point a few Metro stops from St Peters, I would also suggest Ricks Rome walk as a guide.
The progression naturally takes you through all of the major old town sites into the Trajan Forum area, the Forum, and Coloseum at the end.
The best part is the only cost is the Vatican Museum and the Coloseum/Forum Ticket.
I would suggest not doing a tour, only because it is easy to do yourself and this allows you the flexibility to slow down or speed up depending on your own interests.