That, of course, will cover next to nothing in the post-Wittgensteinian analytical camp. But eh, you could do worse if you have one book to read.
Philosophers love formal logic, so that's one thing that's of interest.
Once you have a good understanding of logic, Philosophy aims to investigate important questions that other fields don't seem to have a good grasp of. Here are some of them:
- How can that sensation of redness that you experience when you look at a ripe tomato arise from or be explained by scientific law, which seems to only answer questions that are very qualitatively different from this question? And how do you know that your friend has that same sensation of redness? Perhaps when he looks at a ripe tomato, what he experiences is what you experience when you look at a blueberry.
- If Star Trek transporters work by ripping apart all your atoms and then making a copy of you at the other end from atoms at the destination, would that still be you? Or would you have died, and there be a new person who is deluded into thinking he's you.
- When you push around a wrinkle in your bed-spread, is that wrinkle itself a real thing, or is it just similar different bunches of your bed-spread?
- If you could murder one innocent person to save ten people, would that be the right thing to do? If so, why? If not, why not? What if you could save a million people instead?
http://en.wikipedia.org/wiki/Qualia
"Who is the most original and the most versatile intellect that the Americas have so far produced? The answer "Charles S. Peirce" is uncontested, because any second would be so far behind as not to be worth nominating. Mathematician, astronomer, chemist, geodesist, surveyor, cartographer, metrologist, spectroscopist, engineer, inventor; psychologist, philologist, lexicographer, historian of science, mathematical economist, lifelong student of medicine; book reviewer, dramatist, actor, short story writer; phenomenologist, semiotician, logician, rhetorician and metaphysician. He was, for a few examples, the first modern experimental psychologist in the Americas, the first metrologist to use a wave-length of light as a unit of measure, the inventor of the quincuncial projection of the sphere, the first known conceiver of the design and theory of an electric switching-circuit computer, and the founder of "the economy of research." He is the only system-building philosopher in the Americas who has been both competent and productive in logic, in mathematics, and in a wide range of sciences. If he has had any equals in that respect in the entire history of philosophy, they do not number more than two."
Quotes: http://en.wikiquote.org/wiki/Charles_Sanders_Peirce
Edit: from http://plato.stanford.edu/entries/peirce/, "Currently, considerable interest is being taken in Peirce's ideas by researchers wholly outside the arena of academic philosophy. The interest comes from industry, business, technology, intelligence organizations, and the military"
I think it is important to read Plato closely. It would probably be helpful to have a glance through "Ancilla to the Pre-Socratic Philosophers.
To really understand it, I recommend going through a survey book of Western Philosophy to go through Plato and the other Greek and Roman philosophers, particularly Aristotle. Then move on to the medieval philosophers and toward the likes of Spinoza. Studying the history of Skepticism from Descartes onward, I find to be critical.
You want to familiarize yourself with the famous problems of philosophy (problem of evil, problem of induction, etc).
You may be interested in the philosophy of science, people like Carl Hempel, Karl Popper, Kuhn, essays from people like Gould. I recommend "Readings in the Philosophy of Science: From Positivism to Postmodernism."
This is sort of scattered because it is a broad field. Some people mention the Analytics and Continentals, I would definitely start from the ground before you get into the differences of Pragmatism and Pragmaticism.
A major reason I suggest this path is that if you start reading later philosophers, you are missing an entire context and discussion that goes back to Plato and Socrates, even the Pre-Socratics like Heraclitus.
But, you can do a lot worse than reading "Sophies World" and then skipping to the Philosophy of Science text I mentioned and then filling in the gaps later. This is just one suggestion. :)
One thing I haven't seen mentioned is that often, Philosophers of a certain generation are building their theses in reaction to the previous generation. So there's a great reason to read Ancient philosophy, starting with the pre-Socratics.
I highly recommend "Retrieving the Ancients". David Roochnik (the author) was my professor for both Ancient and Modern philosophy. Trying to be unbiased here but this is a great introduction to the pre-Socratics and it even connects their ancient issues with modern ones.
A good start would be to listen to all the episodes on ancient philosophy, and then to approach the original texts directly, with particular emphasis on the Platonic dialogues. As Whitehead said, "The safest general characterization of the philosophical tradition is that it consists of a series of footnotes to Plato." The Stoics are also very approachable.
In the opinion of my teachers, the pivotal figures in the history of philosophy were Plato, Aristotle, Descartes and Kant. If you master those four, you won't go wrong.
I don't know if this qualifies as "good", but it is certainly interesting: http://paulgraham.com/philosophy.html .
These are what you're looking for. You won't regret either of these.