Recommended Books to start

Plato's The Republic [circa 380 BC] and Dialogues [387 BC] Aristotle's Nicomachean Ethics [349 BC] and Politics [384-322 BC] Rene Descartes' Meditations in First Philosophy [1641] Baruch Spinoza's Ethics [1677] Gottfried Leibniz's Monadology [1714] John Locke's An Essay Concerning Human Understanding [1689] George Berkeley's Three Dialogues beteween Hylas and Philonous [1713] David Hume's Enquiry Concerning Human Understanding [1748] Immauel Kant's Groundwork on the Metaphysics on Morals [1785] & Prolemogena to any Future Metaphysics [1783]

I highly recommend NOT to start off with any contemporary philosophers. This is because the contemporary field is highly specialized and fragmented, and will get you lost. One very important reason not to is that one of the hallmarks of philosophy is to get you to think for yourself, and so it is essential to know the history and origins of ideas and where they come from, and why is it they are as they are now.

First of all, Western Philosophy after Kant in the late 19th century broke up into various strands.

Analytic philosophy

was founded by Frege, Russell, von Quine and Wittgenstein, who emphasized a mathematical approach to philosophy. Their emphasis was on conceptual clarity, linguistic analysis and logical understanding. This led later to Logical Positivism and subsequently to current philosophy as it is now prevalent in Anglo-American universities.

Continental philosophy

includes the field of Phenomenology (Later Existentialism); Hegelism, who exposed a form of Idealism (Marxism and Critical Theory arose as a reaction to this); Freud and Psychoanalytic Theory. Structuralism and Post-Structuralism is in part influenced by Wittgenstein.

The Whole and The Part

Why is it important to know how it all started and begin similarly yourself? Because in the realm of philosophical inquiry, there generally may be what is considered the 'Whole' and 'Part'. It is better to start off with the whole so you can firstly, try to figure out the problems for yourself, and identify what questions concern you the most. Is it the quandary of existence? The idea of a purpose? The question of an ideal society?

Most, probably all philosophy starts off with such questions as relates to our life and existence, relating to us as we are and our mortality. It starts off as speculation and wonder about the nature of things. It is only in the last 2 centuries that philosophy became mathematical and linguistic in nature - partly influenced by the scientific age and its insistence of empirical certainty, partly as a result of a dissatisfaction with vague metaphysical concepts. Modern philosophy tilted towards the material world, in one way or another.

Linguistic analysis

arose as result for our need for clarification in order to understand the underlying meaning behind words so as to understand what we are talking about, that is also an offshoot of the scientific age.

It is not clear however that the answers are to found as we become clearer, or if there is even such a thing as an 'answer' at all. A large part of analytic philosophy, influenced by Wittgenstein, accepts the role of philosophy as simply conceptual clarity. A large part of Continental philosophy rejects that. A good part of both strides both sides. The question remains nevertheless whether the role of philosophy is merely to clarify, or to find specific answers. Normative questions continue to remain important to us, philosopher or not.

Good references

Stanford Encyclopedia of Philosophy. Written by experts in their fields and refereed. Some are quite technical. Heavily analytic but adding a lot of continental topics.

Early Modern Texts. Many ancient and modern philosophy Works translated with erudition and adherence to the original by Jonathan Bennett, an Oxford philosopher.

Contemporary Debates in Philosophy series. Very good series showing both sides of the arguments of philosophical topics, written with clarity and clear explanation. You can actually find some of them free on Google.

Note about Reading Original Texts

If you acquaint yourself with the language written long before, the use of the words may be different, and have a different sense of meaning. Many of these texts however, have good translations. It is important to read them as they are so that you can get a good idea of what those philosophers are trying to convey, and as best as possible, what they mean in the way they say it. Likewise, to get a feel of the concerns of those philosophers in their own time in the way they convey their thoughts to you through their style and language.