For the philosophy of mathematics, a standard reference is Benacerraf and Putnam's anthology Philosophy of Mathematics: Selected Readings. This will provide a good introduction to some of the "traditional" topics in the subject such as logicism, intuitionism, formalism, and platonism. There are of course many important topics not covered. I'd recommend that you also consider something written by Imre Lakatos, such as Proofs and Refutations, as well as Humanizing Mathematics and its Philosophy: Essays Celebrating the 90th Birthday of Reuben Hersh.
For the history of mathematics, there is the encyclopedic book A History of Mathematics by Carl B. Boyer and Uta C. Merzbach. In particular, this book has some good chapters on the early history of mathematics in non-Western civilizations, a topic that was largely neglected in the West until relatively recently. Now, there's another take on the history of mathematics, which is to treat it not just as a subject in its own right but as something that can illuminate and inform the work of a research mathematician. As mentioned by someone in a comment, the work of Harold Edwards is exemplary in this regard. If your students have a strong enough mathematical background for it, I'd recommend the book Galois Theory.
A rather neglected topic is the relationship between mathematics and religion. A good anthology is Mathematicians and their Gods:
Interactions between mathematics and religious beliefs, edited by Snezana Lawrence and Mark McCartney. There are also the fascinating books Naming Infinity by Loren Graham and Jean-Michel Kantor and Equations from God by Daniel Cohen.
Many of your students may be interested in the topic of women in mathematics. There are several books on this topic, such as Complexities: Women in Mathematics, edited by Bettye Anne Case and Anne M. Leggett.
Finally, depending on how much you're willing to venture into controversial territory, you could consider devoting some time to the question of how to promote diversity, equity, and inclusion in mathematics. Especially in the realm of mathematics education, DE&I is a very hot topic—possibly hotter than you want to touch. I confess that I am not au courant with the literature, so I don't feel qualified to give recommendations, but one example I heard about recently (and which has generated heated debate) was A Pathway to Equitable Math Instruction. But perhaps others who are more knowledgeable than I am can provide better guidance in this area.