As I mentioned before, I started with Pyramids. I would not recommend anyone else starting with Pyramids, because that's practically the most standalone story in the entirety of Discworld. It does not really prepare you for the world at large, since except for Death very few characters from that story appear in any of the other ones except in very fleeting moments.
I've always been partial to all the Watch stories, myself. I like all the Discworld novels, but Vimes and Company always seemed to be the biggest beneficiaries of Pratchett's "the world changes and time marches on" bits, with the integration of the Watch, all the new technologies springing up, the exotic locales the 'City' Watch oddly always seemed to go off to, and the shenanigans they got mixed up in. Men at Arms still has the single funniest segment of a book I've ever read aloud to another human being, with the clown funeral (I won't spoil it here...but it is simply fantastic in its execution). Their stories also always seemed to be the most poignant to me character development-wise...the Fifth Elephant in particular, with the philosophical message of "What is more important, the thing or what it represents?" But that's just me. Really, once you start reading them, you'll find one of his protagonists to be your 'favorite' group, but all of them are wonderful in their own way. And if you start earlier, you do see the evolution in the writing. Color of Magic is loads of fun to read and very satirical, but doesn't go particularly deep in terms of thought...certainly not like "Night Watch." That one is an excellent book.
But one of his greatest moments that I will share here is a footnote. One of my favorite bits of business is where a philosopher on the Disc (name eludes me at the moment) states that the easiest course of action is to believe in all afterlives and all gods equally...that way, one of them is bound to exist and be the right one, and you won't get in trouble. The footnote states, after he died, all the Gods of the Disc surrounded him, various horrible implements at the ready, saying, "We know what to do with clever dicks like you."
I just find that line incredibly amusing.