The correct answer is subject.
The pronoun who is used as the subject of a sentence, whereas whom is used as the object (so you can eliminate direct object and object of a preposition immediately). Possessive form of who is whose, so that is incorrect as well. We are left with the subject - which is the correct answer.
The pronoun who is the doer of the action - you can change the pronoun and use a name (Sarah, for example) if it makes it easier for you to determine that it is indeed a subject.