For the philosophy of Mathematics side, rather than the set theory side, I'd suggest:

Philosophy of Mathematics:  Selected Readings; by Benacerraf & Putnam

From Frege to Godel:  A Source Book in Mathematical Logic; edited by Jean van Heijenoort

Logic, Logic, and Logic; by George Boolos

Fixing Frege; by John Burgess

Foundations without Foundationalism; by Stewart Shapiro

New Waves in the Philosophy of Mathematics; edited by Linnebo and Bueno

For their historical interest:

Foundations of Arithmetic; by Gottlob Frege

An Introduction to Mathematical Philosophy; by Bertrand Russell

One book on the set theory side that I can recommend:

Set Theory and its Philosophy; by Michael Potter