Thus Spoke Zarathustra is not a good place to start for Neitzsche. I would go for 'Beyond Good and Evil' and then work your way backwards before tackling Thus Spake.

For ideas about existentialism and secularism I would maybe go for reading Marcuse's 'One-Dimensional Man' alongside Mircea Eliade's 'The Sacred and The Profane'.

Other than that, good old Plato and The Republic is a good introductionary text covering many different areas.

Have fun :)

Thank you! @I like sushi

For Nietzsche, I would take "The Birth of Tragedy" first. Nietzsche himself said that one should start with his earlier works, and then go with later ones. Though Friedrich rejected "The Birth of Tragedy", it's still a great book. And important one.

And it's pretty existentialist. The question of affirmation of life, it's value.