I first encountered the German philosopher when I was in high school in 1950 or so. Something of a misfit and a rebel, I was drawn to his work because it seemed subversive and countercultural. At one point I even sought to emulate Zarathustra by retiring to a remote mountain cabin to commune with nature; I lasted about five days.
Not long after, the Nietzsche franchise, as it were, was taken over by a Princeton professor, Walter Kaufmann, who rightly dismissed the then-common notion that the philosopher was some sort of precursor of Nazism. However, Kaufmann produced a sort of sanitized version in which Nietzsche became a kind of common-sense purveyor of acceptable, but boring truths.
This notion was upset by the rise of the Death of God movement among such theologians as Thomas J. J. Altizer in the 1960s. Subsequently, Nietzsche was adopted by Foucault and other postmodernists. Meanwhile scholars in Germany have published a great deal of additional primary material, which is gradually being translated.
The best place to start, in my view, is “The Birth of Tragedy through the Spirit of Music,” which introduced the fundamental Apollonian-Dionysian contrast. Then one should proceed to the critical works, such as “Beyond Good and Evil.” I do not recommend “Thus Spoke Zarathustra” at all. The best account of Nietzsche’s thought is by Rüdiger Safranski.