If all of this seems too amorphous, I think in part it's because we won't get a real feel for what we're looking for until we do a little looking. Just as in buying a house, the best way to understand what you're looking for is seeing several alternatives; it helps you sort the truly important from the merely desirable.
If we can agree on a set of fundamental requirements, whether these or others, whether a short list or a long one, it'll help sort out people who simply haven't demonstrated the qualifications for the job. Then it's up to us, through interviews, to decide, among a series of qualified people, who is most likely to succeed.