Facebook\'s user id\'s go up to 2^32 .. which by my count it 4294967296.
mySQL\'s unsigned int\'s range is 0 to 4294967295 (which is 1 short - or my math is wrong) a
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.