The next important criterion is good nature.
Imam Reza (a.s.) wrote in reply to a person who had asked him if it was advisable to marry his daughter to a person known for his ill nature, “If he is ill-natured (bad tempered), don’t marry your daughter to him.”ref
The same will apply where the bride-to-be lacks a good nature. Such a woman, though she may be beautiful and rich, would make the life of her husband miserable. She can never be patient in the difficulties that arise in married life.