The correct answer is (B) over. The phrasal verb 'take over' means to assume control or responsibility for something or someone. In the context of the sentence, 'He took over me the minute we met,' it implies that the person attempted to dominate or control the speaker. This interpretation is strongly supported by the subsequent clause, 'But I'm not worried; I can take care of myself,' which suggests a resistance to being controlled.
Let's consider the distractors: (A) off, as in 'take off,' typically means to depart, remove something, or become successful (e.g., 'the plane took off'). (C) against, as in 'take against,' means to develop a dislike or prejudice towards someone. Neither 'off' nor 'against' fits the meaning of attempted control or dominance implied by the sentence's context. Therefore, 'took over' is the only grammatically and contextually appropriate choice.