I'm not actually that picky about what I'll read, so it's not so much the beginning of the story that makes a difference to me unless there are screaming errors that I just can't read past, but what moves a story to the 'recommend/re-read forever!' pile is when I get to the end and I want more, not because the story feels unfinished but because it was so well crafted that I just want to spend more time in that world with those characters even though the central conflict is resolved.