Ceridwen

Really, I think many of the best short story collections I've read have been text-book-y: the Oxford this or the Riverside that which I bought for classes lo, those many years ago. I can't find the one I had from a class on the subject of the short story, but that was great. I would give props to the Oxford Book of Gothic Tales too. There are quite a few hard to find short stories in there that are fantastic, plus the introduction is wonderful. 

In the single-author category, I'd cheat and go with Burning Your Boats, which is a posthumous collection of most, if not all, of Angela Carter's short fiction. It includes both The Bloody Chamber and Black Venus (which was tepidly retitled as Saints & Strangers in the US), which, by themselves, are wonderful collections. 

*Sorry. As an American, I have real trouble with that supernumerary u in words like favourite. It just doesn't feel natural. But I guess its Book A Day UK, not Book a Day USA, so I should suck it up. If you're curious, like I was, how we ended up with different spellings in different countries, even the wiki page on English-language spelling reform is a good start. Or the essay often attributed to Mark Twain, "A Plan for the Improvement of English Spelling." Twain did tangle with Andrew Carnegie over the subject of spelling reform, with the latter spending large amounts of money in an attempt to reform spelling, so it's a sensible attribution. Doesn't really sound like him though. Um, anyway, tangent....