무슨 and 어떤 have a very small nuance. 무슨 means something like "I have no idea which ones there could be" - 무슨 음반이 있어? = what/which albums do you have? (could be anything)

어떤 means something like "of the few obvious choices, which one?" - 어떤 영화 볼까? = which movie should we see? (if you're at the movie theater, there are around 7 choices)

My understanding is 어떤 is a better word to use here. I'm not native and could be wrong.

If by "question word" you mean 무슨, it goes before the subject

It's a cutural/language difference thing at that point. In English, you would never ask "What kind of hamburger exists?" if you were, say, asking this question at a restaurant. So the "you" in that sense is implied in that it is interpreting the meaning of the sentence rather than providing a word-for-word translation.