I basically got into Holmes as a complete mess – found 'The Hound of the Baskervilles' first because it was a standalone movie, then stumbled into 'A Study in Scarlet'. If you're aiming for a proper experience, publication order is the move. Start with the novels: 'A Study in Scarlet' introduces Watson and Holmes meeting, 'The Sign of the Four' comes next, then you can jump into the short stories.
The first two short story collections, 'The Adventures of Sherlock Holmes' and 'The Memoirs of Sherlock Holmes', are where the character really hits his stride. After that, 'The Hound' is a novel again, then the later collections like 'The Return' and 'His Last Bow'. The publication order isn't just chronological; you see Conan Doyle's writing evolve, and the little references between stories actually land. Skipping around ruins some of the callbacks, like the mention of the 'Giant Rat of Sumatra' you only get if you've read the earlier ones.
Honestly, 'The Case-Book' can feel a bit uneven, but it's worth it for a few gems. The whole thing is a slow build of their friendship, which gets dismantled if you read out of order.