Because Facebook assigns the IDs, and not you, you must use BIGINTs.
Facebook does not assign the IDs sequentially, and I suspect they have some regime for assigning numbers.
I recently fixed exactly this bug, so it is a real problem.
I would make it UNSIGNED, simply because that is what it is.
I would not use a string. That makes comparisons painful and your indexes clunkier than they need to be.