"A Scandal in Bohemia" is a very good one to start, for a short story fast read. My husband's favorite is "The Red-Headed League." "The Reigate Puzzle" is one in which Holmes does some clever things to foil inept local authorities from screwing the pooch. Another one I like quite a lot is "The Adventure of the Illustrious Client," though it is one of the much later stories. "Hound of the Baskervilles" is another fantastic one, but it is a novella, and about three or four times as long as the short stories.
They're ALL good! I enjoy the intricacy of the stories and the training they give one in learning that what you see is not necessarily the reality of things. Even more, I enjoy and ponder the skill of Conan Doyle of in telling the story. It is very fine writing and constantly instructive.