Bossk id also recommend Nietzche and Sarte. I primarily recommend existentialism to people when they are first getting into philosophy. I feel like its a lot more relevant for people - I mean, it tackles questions that have import to most everyone.
But you should also consider some more foundational stuff. Descartes, Hume, Locke. From them you will get an idea of the foundations of contemporary philosophy. Older, "classics", like Plato, Aristotle, Aquinas, etc. are important, but I dont feel, as relevant.
Regicidal, what do you think of Dante? And have you by chance read any of Virgil's work?