Great Short Stories of the World (selected by editors of The Reader’s Digest) is a perfect book to introduce newbies to the works of classic short story writers. You would find some of the finest writers of early 20th century in this book. This book is bound to make you wonder how complete in itself a short story can be. And yes, it is a testimony to the fact that short stories can be as much fun as reading a novel.
This is a 800 page book with 71 stories (a dozen abridged by the editors) in it. Finishing it off at one go might ruin the experience. So come back to it once in a while.