As others have said Mort and Guards, Guards are both great places to start, I would also add Equal Rites to that as well and also Wyrd Sisters (although thinking about it, I would probably suggest a newcomer start with Wyrd Sisters rather than Equal Rites).
Some of the books are almost like a mini-series within the whole thing and, if you find those particular characters engaging then it may well be worthwhile reading all those in order.
For example, if you started with Guards, Guards and wanted to follow those characters then the next books to read would be:-
Guards, Guards
Men at Arms
Feet of Clay
Jingo
The Fifth Elephant
Night Watch
Thud
Snuff
Or if you started with Equal Rites or Wyrd Sisters then the books following these characters are:-
Equal Rites
Wyrd Sisters
Witches Abroad
Lords and Ladies
Maskerade
Carpe Jugulum
If you enjoyed Mort and wanted to follow these characters then the next books would be:-
Mort
Reaper Man
Soul Music
Hogfather
Thief of Time
Once you've got a feel for the world from some of these books then I would also suggest the couple of books featuring a character by the name of Moist von Lipwig:-
Going Postal
Making Money
There are also a number of stand alone books that it does help if you have read some of the above first. I particularly enjoyed:-
Moving Pictures
Pyramids
The Truth
Only then would I suggest going back to the original books that started it all. In order they are:-
The Colour of Magic
The Light Fantastic
Sourcery
Eric
Interesting Times
The Last Continent
Unseen Academicals
The Last Hero
Then for younger readers I would also recommend starting with the series that he did specifically for younger readers set in the same world:-
The Wee Free Men
A Hat Full of Sky
Wintersmith
I Shall Wear Midnight
The Shepherd's Crown