As /u/ajr82 mentioned, this is a very popular question and my own thoughts can be found here. It's a reasonably accurate narrative of Later Roman political history, but it missed on so much more, such as social and cultural history, as well as new approaches such as the usage of prosopography and archaeology. It doesn't help that Gibbon's thesis is demonstrably wrong, as Christianity was evidently not the cause of moral decline/decadence of Roman society. There is no reason to start learning about Roman history with his book when there are so many other options, all written for the general public and can be found in local libraries/bookshops, such as:

• Peter Heather, The Fall of the Roman Empire: a New History of Rome and the Barbarians

• Peter Heather, The Restoration of Rome: Barbarian Popes and Imperial Pretenders

• Adrian Goldsworthy, The Fall of the West: The Death of the Roman Superpower

• James O'Donnell, The Ruin of the Roman Empire

There are five seperate questions in the FAQ that should give you a very thorough answer to this.