Discworld has a number of major story arcs which are generally able to be read separately although they often overlap, and so some people prefer to follow one of the many Reading Guides out there to determine which books to read and when.
But a lot of us disagree and say that you should go to the very first book, The Colour of Magic, start there, and read the whole series in order, because it lets you experience Pratchett as he evolves from a pretty good writer into one of the best fantasy authors of all time. Plus you get to experience the Discworld itself evolving, as the Disc is broadly an allegory of Earth in the 1700s / 1800s with many of the same technological progressions.
It's important to note, though, that the first few books in the series can be tough to get through if you don't already have an appreciation for what's coming, and some readers are put off by them, but please, please don't give up, you have no idea what you're missing right now.
God, I envy you so much. If I had three wishes, I would genuinely spend the third one on forgetting the Discworld series just so I could once again experience the joy of reading it for the first time.
I would also highly recommend reading The Annotated Pratchett[1], which provides insight into the many fascinating real-world events, objects, people, myths, legends, and more that Pratchett subtly (or not so subtly in some cases) referenced in his work.
Don't get ahead of yourself of course, wait until you've finished reading the entire book before you read its corresponding APF entry so as to avoid spoilers :)
I think it doesn't matter a great deal, the plot of each individual book is usually pretty freestanding, so it's a question of whether you want to watch the characters develop chronologically or not.