The problem with even that level of description, is that characters change. I don't think I've actually had a toon that developed in obediance to any plan I might have had for them. So describing toons so GMs can jigsaw us together is somewhat unproductive, since toons and plans change. Even parties change, with people dropping and replacements coming on.
If I put myself in the place of the GM, I think I'd be trying to check off, or double- or triple-check off, broad functions, maybe...?
Can Heal, Can Hurt, Can Take It, Can Steal, Can Wheel&Deal?
Father, Fist, Fort, Fingers, Face, ...Fireball?
Whatever we might agree on, somebody will show up who doesn't fit. Call them 'Fancy', maybe. :)
I know my Monk, who in a previous aborted playthrough dipped Magus, doesn't think of himself as a 'Martial', but he's not, at level one, anything like 'Skilled', and even after dipping, isn't the party's 'Arcane'.
The real issue in the list you were making was the thirty-five applicants, with people like my monk and the face-arcane summoner and her scout-ghost eidolon. That's Fancy. :)
Am I a Lion? I don't think of myself as a Lion...