May the first wife herself choose a second wife for her husband?

Yes — there is no prohibition, but it is not required by the Shariah; only a small number of wives choose this path. A wife who is involved in choosing may be more confident of the candidate's character and find it easier to accept. Even so, the candidate must still consent freely, and the husband still bears all the conditions of fairness and must apply for the court's permission. Never feel compelled to do it to prove your 'sincerity'; it is a personal choice, not a measure of faith. Also make sure the candidate is not among the women who may not be married together, such as the wife's sister or aunt. See criteria.