How Sam Read the Discworld Books.
I'm not including the Tiffany books because I haven't read them. I've heard they're excellent. Also excellent are the YA "Bromeliad" trilogy, featuring Nomes who live in a department store until they make a gallant bid for freedom. They're not Discworld, but well worth reading, and appropriate for younger readers.
There are several series arcs in the Discworld books, as well as standalones. I recommend trying a standalone or two before you decide whether or not you want to try the series arcs. Characters all cross over each other between books, too, but basically you can pick up any Pratchett book and enjoy it. You'll just enjoy it a lot more if you've read others -- Night Watch, for example, is MUCH more interesting if you've read Feet of Clay, because you'll know Vetinari better and it'll be more interesting to see him as a teenager.
Small Gods -- Standalone
Pratchett's take on comparative religion. The predominating religion in the book, Omnianism, also reappears in the Watch books as a running joke. Small Gods is set about a hundred years before any other book -- the rest all take place over the course of about a forty-year span or so. More like a ten-year span if you don't count the time travel in Night Watch.
Pyramids -- Standalone
I come back to this one over and over again because I love the sections about the Assassin's Guild. Pratchett tackles Egyptian mythology/theology. The Assassin's Guild is good to know; it crops up in a lot of the books. This is also the book in which we meet Prince Pteppic, who is a much-beloved character (and where Pratchett takes his "Pterry" nickname).
If you like these two you'll probably like most of what Pratchett writes. The serieses are:
The "Watch" series
The Watch series is my personal favourite. Some of Pratchett's most complex heroes and heroines -- Vimes, Sybil, Vetinari, Carrot, and Angua -- grew out of these books. They focus on a small cadre of Watchmen in Ankh Morpork, the biggest urban centre on the disc, as they slowly rise from obscurity to lesser obscurity. Their hero, Vimes, is a hard-boiled, cynical, mean-as-nails police captain and he's an utter joy to read. Vetinari also shows up most often in these books, though he appears frequently in the Wizard books as well.
In which Vimes and his sad Night Watch take on a DRAGON.
Men At Arms
Pratchett's take on the firearms debate. Also marriage, gender equality, and werewolves.
Feet of Clay
Vimes chases an unnatural murderer while Vetinari, the Patrician (ruler of the city) is slowly being poisoned. Pratchett addresses racism.
Ankh-Morpork prepares for war, and Vimes attempts to prevent it. Deals with war and motivations for war, and also has my all-time favourite literary allusion to Ozymandias in it.
The Fifth Elephant
I can't describe my love for this book. Vimes goes to Uberwald (basically Transylvania in every bad vampire film ever) and gets embroiled in local politics. We also meet Lord Vetinari's former paramour and Angua's family.
Nominally a Watch book but really a standalone, The Truth is Pratchett's take on journalism. It introduces some favourite characters, including Otto the Black Ribboner and William de Worde.
The Night Watch
One of Pratchett's best books, IMO. Vimes is flung backwards in time, and finds himself mentoring his own younger self in the dark days before the rise of Vetinari. Both Vimes and Vetinari make appearances as adolescents, and Les Mis is satirised, among other things. One of Pratchett's darkest and most complex novels.
I read this but haven't retained much of it. There was a lot about Dwarves, and we meet Sam Vimes Jr.
I feel like Pratchett got back on track with this one, which is about Vimes and his family on a country holiday.
The "Death and Susan" series:
Death, the character, appears in almost every single book. He's the anthropomorphic personification of death; he has the robe and scythe and all the rest. He's also very much linked to archetypal mythology -- many of the books discuss the origins of modern day rituals such as Christmas. His granddaughter Susan is an exceptionally good female character, like Angua in the Watch books.
In which Death takes an apprentice who, predictably, bollockses things RIGHT up.
To be honest, this may come before Mort; there's no Mort mention in it. It's about Death taking a holiday.
This is the one where the Death series really starts to take off in my view. Susan, Death's granddaughter, meets a young Musician named Bud-y-Holly. Pratchett tackles the rise of rock-and-roll, Discworld style.
Pratchett addresses the historical traditions of Christmas. This is both a hilarious book and also rich with mythological symbolism.
The Thief of Time
A maniac invents a clock that might destroy the universe. Susan and an unusual companion must destroy it. Sort of a kung-fu movie meets mythology. Apparently it has a lot of Reservoir Dogs references.
The "Witches" series
The Witches series is predominantly about the power of ancient myth and fable, especially in the rural hill cultures of Great Britain. It follows two elder witches (Granny and Nanny) and two younger witches (Magrat and Agnes), though their husbands and sons occasionally make brief appearances.
Both a Witches and Wizards book, but it's predominantly the Witches. You can read the rest of the series without reading this one; it's not very memorable in my opinion.
Something akin to Macbeth, and one of Pratchett's best books about hill country mythology and also theatre.
Magrat, the dubious heroine of Wyrd Sisters, becomes a Fairy Godmother. Pratchett tackles Faerie Tales.
Lords and Ladies
The witches battle the Fey. Who aren't as nice as one would think, really. People who do morris dance will get an especially big kick out of this one.
The Witches go to Ankh-Morpork (setting of the Watch books). Pratchett satirises Phantom of the Opera. A couple of the Watch show up in cameo spots. An excellent book for Phantom fans.
The Witches battle vampires. A really interesting take on vampirism. This also gives the origin of the "Black Ribbon" which shows up again in the later Watch books, particularly The Truth.
The "Wizards" series
The Colour of Magic and The Light Fantastic
Two halves of one book. Heavy on the satire of fantasy and scifi novels. Not his best work, but then they were his first two books.
Wizards at war. Still very fantasy-satire oriented.
Pratchett does Faust. Pretty funny. Faust is replaced with a ten year old. A short and easy read.
Could also be considered a standalone. Pratchett satirises the rise of the movie industry and the golden age of film.
Rincewind, the nominal hero of the Wizard books, travels to the Discworld analogue of China, and helps a peasant revolution. The way Pratchett handles Chinese culture made me somewhat uncomfortable.
The Last Continent
Rincewind moves on to Australia, or its equivalent, and uh....does...stuff. It's a really funny take on Aussie culture, but I can't recall the plot.
The standalones (other than Pyramids and Small Gods) are:
The Truth (Nominally. Could be considered a Watch book)
Monstrous Regiment (Has Vimes and de Worde in it, but not really a Watch book)
Moving Pictures (Could be considered a Wizards book)
Going Postal and Making Money
A pair of novels about Moist von Lipwig and his accomplice Spike. Going Postal, about von Lipwig taking over the Ankh-Morpork post office, is a little slow moving at first, but picks up quickly and really gallops along towards the end. Making Money is a light, fast-moving novel about von Lipwig moving on from the post office to the royal bank. Vetinari features heavily in the second book. Set in Ankh Morpork, setting of the Watch books.
Commentary post-hack: Thanks to danceswchopstck, light_of_summer, and salammoniac for helping me recover this!