The imperial forums are a series of big places. I recommend to visit the Cesar's Forum, the Auguste's Forum, the Nerva's Forum, the Trajan's Forum and The temple of the peace.
Even you didn't reserve hotel in Rome you will find plenty of hotels and hostals near to Termini station...go to Via Gioberti, Via Principe Amedeo...
Travel by metro. Underground is the way to go. It is so much cheaper. It may not be the nicest of places, but if you're on a budget it is the best way.
We went all around Rome and up to Florence and Pisa all by train. It was marvelous.