Is it a good idea to use fb.me over facebook.com in advertising material?

Apologies if there's a better Stack site for this, but I can't think of what it could be.

I'm designing some flyers for an upcoming side business of mine, and need to include a link to my Facebook page on these flyers.

As far as I can tell there are just two ways that I can do this:

• facebook.com/MyBusinessName
• fb.me/MyBusinessName

For the purposes of brevity and ease-of-typing, I want to go for the latter, but I'm wondering whether there might be any implications of doing so, user experience or otherwise.

For example, are users likely to be more suspicious of typing in the unfamiliar fb.me link as opposed to a facebook.com one?

The target audience includes enterprise users, so how likely is it that the relatively unknown fb.me will be blocked behind corporate firewalls whereas the standard Facebook one won't?

As a very related question, is it necessary to include a link at all? Would the Facebook page's name alongside a Facebook icon suffice for the average user?