You're entering deep water! Gibbon is interesting as an example of someone reflecting on a classical empire at a time when the British Empire was undergoing radical change (late 1700s), but we know more (e.g. archaeology, better access to manuscripts, new methods of interpreting texts), and many of his conclusions are out-dated. You might want to check out the FAQ on the decline of Rome and see what sources are cited there. There's also a handful of relevant reads in the book list.

There's wide divergence of opinion on whether the western Roman Empire even fell. On the one hand, you've got works like Walter Goffart's Barbarian Tides and Bryan Ward-Perkins's The Fall of Rome and the End of Civilization (the titles speak for themselves). On the other, you've got Peter Brown's The Making of Late Antiquity and The Rise of Western Christendom (same period, very different focus). There's a bunch of different problems rolled up in discussing the fall of Rome: Did the 'barbarians' actually have a distinct sense of ethnicity, or did they see themselves as Roman mercenaries? Did Christianization dramatically change Roman society, or did it simply give a new vocabulary to the same old systems of patronage?

For a historiographic paper, your best bet for effective and efficient research (unless you've got the time to read this rather hefty literature) is looking at book reviews. Guy Halsall's "Movers and Shakers: The Barbarians and the Fall of Rome" might be one good launching point. Your university library website should have a way to search just for book reviews (usually listed under articles). Talk with your reference staff if you need help (your tuition pays their salaries!). Search for any of the names above, and other names worth knowing might be Peter Heather, Patrick Geary, Chris Wickham, and Robin Fleming. Note that most of this literature tends toward a focus on Gaul and Italy, and the debates are different for Britain, Spain, and North Africa. Averil Cameron and Garth Fowden have also written relevant material, but their focus in on continuities in the Eastern Empire, as well as contacts with Islam. (Fowden's Before and After Muhammad has a very useful, if somewhat dense, chapter resuscitating some of Gibbon's ideas about Islam, which might also be of interest.)

Reviews of anything these people have written (or book reviews by these people) will give you the kernel of their argument in just a single page or two, and it will save you some time hunting in the stacks. Then you can decide which books seem most important for your take on these debates, and you can work through their introductions and arguments from there. And as always, once you've got a direction for your research, bounce your ideas off your instructor. S/he'll love to hear from you!