Introduction to Philosophy by Nigel Warburton provides a nice overview of the various aspects of philosophy, ranging from stuff like Descartes to stuff like Hobbes.
The Problems of Philosophy by Bertrand Russell is a fantastic little book. Very easy to read but incredibly well written, with a lot of very interesting ideas in.
Descartes - Meditations is normally where people recommend you start, and is fairly straightforward.
Plato and Aristotle should obviously be on your to read list, with Republic by Plato, and Nichomachean Ethics by Aristotle, both worth a read.
If you're interested in existentialism, then as Surfer says, check out Sartre, Camus and Kafka, although Sartre can get rather complex and weighty.
Michel de Montaigne is good too but I guess you're after the existential kinda stuff so he isn't massively appropriate.
Edit: Just seen that PJW has said Nietzche...I'd say stay away from Nietzsche until you have at least a basic foundation of philosophical ideas because you'll either mis-intepret Nietzsche or just not understand it.