I think Alejandro1 gave a good answer as well, but my answer will be slightly different.
I'd suggest starting with An Enquiry Concerning Human Understanding if you're more interested in epistemology, or otherwise An Enquiry Concerning the Principles of Morals if you have greater interest in the foundation of morality, ethics, justice, etc.
As the familiar story goes, Hume wrote A Treatise of Human Nature, and then found the reception for this work to be extremely unsatisfactory (everyone seemed to misunderstand it, and many just ignored it). He decided that this was a matter not of the content, but of the writing style and quality, and thus set out to recast his most important insights in a fashion that would be more readable, engaging, etc. In this way the Enquires mirror the Treatise, and are a restatement of what he deemed most important and interesting.
But what I should mention is that although it is the case that the Enquires restate a lot of the content of the Treatise, and that they're much more readable, at the same time I would say that they leave out a lot of the most important content in the Treatise, and they're a lot more impersonal and less autobiographical. The Enquiries are very insightful, and very easy to read. The Treatise on the other hand is ridiculously difficult to read, but once some of the key pieces are understood, it becomes an incredible, introspective journey through the mind of who I consider to be most likely one of the most rational, lucid, insightful, brilliant people in the history of civilization.
The Enquiries are absolutely wonderful, and a perfect example of some of the most lucid, insightful non-fiction prose in history. But I consider them in a way to be somewhat of a stepping stone or reference for understanding what's contained in the Treatise. I would recommend starting with the Enquires, beginning with whichever seems like it would be more interesting for you personally, and then moving onto his much deeper, much more difficult, much more autobiographical work: A Treatise of Human Nature.
Since LessWrong is a major congregation point for certain philosophical ideas, and because people here tend to be more objective (in the sense of not being self-deluded) than elsewhere, I thought I'd ask people's views.
To be clear, by "Greatest Philosopher" I am referring not to the most correct philosopher in human history but the one who deserves the most credit for advancing human philosophy towards being more true.
Off the top of my head I would say that a prime candidate would be Hume- amongst other things he rejected the idea of a soul, realised to a much greater extent than his predecessors the limits of human knowledge, and opposed the idea that reason is somehow an objective force that can make priorities independent of emotions.
Aristotle deserves considerable credit relative for his time but doesn't make the list because although it wasn't his fault his ideas were dogmatically accepted and held back both science and philosophy later on.
Your thoughts?