I tend to disagree with all those commenting to you. If you want a broad understanding of philosophy, well there is a lot to it, so "where to start" is a loaded question. It is not like Plato or any particular philosopher is a one-stop-shop . If you have an expertise in physics, well you didn't master it from just one book. I recommend starting with the novel "Sophie's World;" it is very accessible and it can give a good springboard for what to study next.

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. :)