"The Itinerary" by Roberta Isleib, in Mystery Writers of America Presents The Rich and the Dead, edited by Nelson DeMille.
So, what does the beginning of a short story need to do?
One thing only, really. It has to convince the reader to keep reading, not to abandon the story in favor of the next one in the book, or a trip to the supermarket, or the latest installment of Real Crap of the Cable Networks.
The opening can and probably should do a lot of other things, but keep- 'em-on-the-ranch is the one necessity. Let's see how much Roberta Isleib manages to accomplish in her first paragraph.
Detective Jack Meigs knew he'd hate Key West the moment he was greeted off the plane by a taxi driver with a parrot on his shoulder. He hadn't wanted to take a vacation at all, and he certainly hadn't wanted to come to Florida, which he associated with elderly people pretending they weren't declining. But his boss insisted, and then his sister surprised him with a nonrefundable ticket; he was screwed. A psychologist had once told him that it took a year for grief to lift and that making major changes during this time only complicated the process, which was why he'd gone to work directly from the funeral and every day in the three months since. There was no vacation from the facts: his wife Alice was dead and she wasn't coming back.
In 130 words we have learned a lot about the protagonist (an older cop mourning his dead wife), the setting (the bizarre end of Florida), the mood of the story (I absolutely love "he was screwed"), and the possible plot (a busman's holiday story).
And that's exactly what it is. Meigs, a thousand miles from home and off duty, witnesses an argument and the next day recognizes that one of the quarrelers is the missing person in the newspaper story. He spends his vacation solving the case - which goes in a direction I would have never guessed.
Did the paragraph do its main job? Every reader has to decide that for themselves, but it certainly kept me reading.