At the bare minimum, offer FB, Google and Twitter so people don't feel like they're coerced. (And you'll be surprised how many "not likely" people use a decent application if it's useful and you don't send them away).
My guess is that 90% of potential user will go away when you force them to use FB, whereas 70-80% of your potential user base will still find something not to like when sign-in is not a problem. (i.e., think about the conversion ratio from people who learn about your site to people who either go "ooh, I'm going to try this out" or "hm, looks interesting but whatever" - people are often walking a thin line between these options and shifting the line by making trial and sign-up as easy and convenient as possible will get you more conversions).
Otherwise, if you're willing to put your soul into FB's hands, do the full monty and structure your app as a facebook app. If you don't think that would be a good idea, think about why you're only targeting facebook users. (And do remember that "facebook demographic" and "actual facebook users" are very different things).