The key to understanding the poem "My Last Duchess" by Robert Browning is to understand how Browning uses the conventions of the dramatic monologue. In this, as in most of Browning's dramatic monologues, characters' self-revalations usually end up showing how under what might appear to be conventionally successful or normal exteriors lie hidden flaws. In the case of the Duke, he is often described by literary critics as a "collector", of people and riches as well as art objects.
In the way the Duke describes his last and next duchess, we get a sense of his extreme possessiveness and the way he values objects as symbols of his status. When he gracefully states that the daughter's "fair" (attractive) self will suffice, and that he will be satisfied with a reasonable dowry, his graceful phrasing masks a desire to negotiate as large a dowry as possible. He also is thinking of his future wife as an ornament like his art objects in appreciating her physical attractiveness.