The was für construction is maybe a little odd on the face of it, but shouldn't be so foreign to us Latingesprechengemenschenundfrauernheit.
Generally speaking, as far as Indo-European is concerned, interrogative words have highest priority in an utterance, apart from a vocative (of which it may be said truly: 'it has no grammatical bearing on the sentence'). This is still the case in English, unless you're aiming for a certain affectation ("(And) You're doing what, chastising me?!") So, a preposition or similar particle is bound to become 'post-positive' (τίς τ' ἄρ σφωε θεῶν... quem penes est uirtus).
In the case of German, this syntagm became a(n indeclinable) determinative, so that it may even itself be modified by a preposition:
Mit was für einer Person haben Sie gesprochen? (example taken from my German grammar book).
It is also not uncommon for the neuter form to become indeclinable in predicative use (cf. colloquial Russian: Что такое эти звери? 'What kind of animals are these?')