Puella Magi hunt Witches. Witches hunt humans who are in despair.

As for the state of one's soul before they contract - the Soul Gem would, of course, be clean initially. If someone has suffered before they contract, it simply means they'll be a stronger Puella Magi compared to their fellow Puella Magi.

_{[There was the flick of an ear as he pressed his front paws gently into her thigh.]}

You're worried about the state of your soul, aren't you?

_{[It was rather obvious, really.]}