The first official Discworld book is The Colour Of Magic, which leads directly into The Light Fantastic. There IS a continuity, but each book focuses on a different character or group of characters, like Rincewind the wizard who can't even spell 'wizard', Granny Weatherwax and co., Death and his granddaughter, the City Watch.... You don't necessarily need to read them in order, but it can help.
I'd recommend trying a selection of the books and following the storylines of whichever characters you like the most, my personal favourites being Rincewind and Death.