I guess I'm not exactly sure what you mean by 'connect with Facebook'. Do you mean what account should 'own' the Facebook Application or page, or do you mean what user you should log in with to other people's sites, or do you mean what link the "Like" buttons should go to? There's a lot of confusing variables to take into account, and I'm not even sure I'm the right one to answer, since your own circumstances and promotion methods are what's important.
However, your last choice is what I think most users choose.. even though, like you say, it's not completely kosher in Facebook's eyes. I personally have a "personal" facebook account in my name, but also a 'business' account under the name "Alex SourceCoast". Not exactly right, but that last one is the one that owns our SourceCoast Facebook application and page.
Hope the helps, but of course, I wouldn't ever recommend violating Facebook's ToS.. so do what you feel is best for your business!