Which logic is most fundamental?

Question

A couple of my introductory logic books appeal to modal and set-theoretic notions in building up first-order logic. (They explicitly acknowledge these connections and say, for example, that validity is a modal notion, or they speak of “sets” of propositions, using the term in an expressly technical sense.) How do these different logical systems relate to each other? Do modal logic and set theory “flow out of” first-order logic? Or is set theory the foundation of all of logic? Or are they somehow or other interdefinable?