The History of the Decline and Fall of the Roman Empire by Gibbon is probably overkill and definitely dated. So I would suggest Duncan B Campbell's The Rise of Imperial Rome, AD 14-193 or Michael Grant's History of Rome. Especially the later for a good overview.

Luckily for you we've got the wonderful Book List! It's not comprehensive, of course, since there are dozens and dozens of books like that, but it is a very good place to start.