Big Sherlock Holmes fan here. You're are lucky in that Holmes books are usually free or very cheap on Kindle.
The first Holmes story was A Study in Scarlet and is longer than the usual Holmes adventures, bar the longer stories such as The Sign of Four and the most famous of all, The Hound of the Baskervilles.
The book can bought on kindle for 77p. I recommend The Adventures of Sherlock Holmes (Illustrated) (Top Five Classics) for the first 12 adventures. The Baskervilles is also available for 77p.
If you want print, then I recommend Sherlock Holmes: The Complete Stories (Wordsworth Special Editions). It's about a fiver.
Holmes stories are very easy to read. Some people assume the language is going to be typical of the era and not as fluent and easy to understand as today's literature. However, Conan-Doyle seemed to write slightly ahead of his time and the stories flow freely with no complicated flows or language at all. I think that's one of the reasons they became so popular in the early 20th century.
Deffo read the Baskervilles. The book is so much better than all the film versions I've seen.