Cat Valente (author of Palimpsest, which is a Hugo nominated novel) is currently editing for Apex Magazine. She has a few choice words to say about the opening paragraphs to any creative writing.
Your opening should be something which hooks the reader. I've read a few times now that every novel should have at least three hooks - one in the first paragraph, another by the end of the first page, and one by the end of the first chapter, so that any reader brave enough to tackle the first few pages will get sucked into the story so fast they barely have time to slap their cash on the counter before they're off to a day of walking into sign posts and going "huh?" whenever someone dares to disrupt their reading daze.
This is valuable advice. It's advice I've been using. My poor friends have had the same three paragraphs about twenty times now, sometimes with only one word changed. But it might be a key word. It might change the tone, tense, or meaning of the entire passage. I'm lucky to have such patient, and critical friends.
I have read hundreds of short stories this year, and it gets easier and easier to tell by the end of the first paragraph, or the first page, whether the author has craft enough for their idea, of if this will be a story that appeals to me.
I also note flagship stories in anthologies. The very first story in an anthology is a statement. It stands proud to represent the stories that come after it. It should be the best story in the book. If not the best, then it should be the most indicative of the anthology's tone. The first story is guaranteed to be read more than any other story (except in exceptional circumstances).
The opening to anything is a powerful statement. Make it the best statement you possibly can.