For a good narrative history, I would recommend Peter Heather's The Fall of the Roman Empire: a New History of Rome and the Barbarians, followed by his The Restoration of Rome: Barbarian Popes and Imperial Pretenders if you are interested in what happened after the fall of Western Roman Empire (which is fascinating by the way, all sorts of people still stuck to the idea of Rome for centuries afterwards).

For a more general overview of the whole period, Peter Sarris' Empires of Faith: The Fall of Rome to the Rise of Islam, 500-700 is really good. It's a bit more academic than Peter Heather and covers a lot more, but I think to understand the decline of the Western Roman Empire, you really have to understand what happened in the vigorous Eastern Roman Empire too, which this book does a great job in describing.