I disagree slightly with those who say the mysteries aren't standalone. The plots are, mostly. You could read 'The American Agent' and follow the murder mystery. But you'd be completely lost on why Maisie is so reserved, what her history with Scotland Yard is, who the people in her office are, and why her personal life is the way it is. The emotional weight comes from the sequence.
Therefore, publication order is the only way to get the full, intended impact. It's a novel-sized character study spread over sixteen books.