The Essentials of Sherlock Holmes
In (hopefully) chronological order. Essential plot points are marked with a *. All links are from Project Gutenberg, unless marked otherwise.
A Study in Scarlet * - Holmes and Watson meet, and their first case together. [Novel]
The Adventure of the Speckled Band - In which Holmes says 'knocked up' twice in a row and I giggle like a little girl. Period talk, I know. I'm awful.
The Greek Interpreter - We meet Mycroft, and Watson goes on about Holmes being heartless.
The Sign of the Four * - The accounting of how Holmes and Watson meet Mary. RE: the new movie, keep in mind that Watson does not have to be a reliable narrator. Food for thought! [Novel]
A Scandal in Bohemia * - The only story with Irene Adler in it; make of it what you will.
The Adventure of the Dying Detective - One of my personal favorites, and there really is no plot. Just subtext.
The Hound of the Baskervilles - Probably the most famous and most quintessential of the Holmes works, and my personal favorite. [Novel]
The Final Problem * - ...Well, if you don't know, I shan't spoil it for you. I will say that this is absolutely essential. Even if you read no other Holmes story, This. Must. Be read.
The Adventure of the Empty House * - it's kind of 'The Final Problem: Part Two'.
The Adventure of the Six Napoleans - Lestrade. That's all I have to say.
The Adventure of the Cardboard Box - Some beautiful Holmes and Watson interaction.
The Adventure of the Bruce-Partington Plans - Mycroft, mystery, and Holmes is emotional.
The Adventure of the Devil's Foot - Another personal favorite, and one of the sweetest scenes I've ever read.
The Adventure of the Three Garridebs - this is not on Project Gutenberg for some reason, possibly because The Casebook of Sherlock Holmes is shit is... questionable, but nevertheless it has this story, and this story contains the most beautiful tribute to Holmes and Watson's relationship and how it has developed.
Of course, I highly recommend reading EVERYTHING~, but if you just want a place to start, this is it!