Check out Italian railways on <a href="http://www.trenitalia.com/en/index.html" target="_blank">http://www.trenitalia.com/en/index.html</A> . You can buy online. Its a long journey of between 5 and 7 hours, depending upon routing, so unless you like sitting on a train all day you might want to think about the overnight train and get a bunk.
Unfortunately I have no recommendations on hotels in Rome.