One thing I'd be need to know, before volunteering to critique anything, is the ambition level of the work. Where does the author intend the work to go? Is it just fan fiction? Or an original work that he intends to put up on the web for free where it will drown among the crud? Or does he intend to submit it for approval to gatekeepers who vouch with $$$$ for the basic quality of the stuff they publish?
Word count is also important. I honestly don't understand the purpose of short stories. There's no time for characters and no time for world. Others are the exact opposite.
Genre is also important, meaning science fiction, fantasy, horror, western, and so forth, but mood is probably at least equally important. Is the story supposed to be funny, exciting, erotic, fear-inducing?
Major tropes can help too. I'm rather biased against stories that don't feature badasses. Others intensely dislike high-competence protagonists. Perhaps this is important enough for so many potential critiquers that it'd be useful to indicate the competence level of the protagonist(s), on some kind of sliding scale (AFAIK there's no article for that yet).
People who ask for feedback on a story often want different kinds of feedback. I'm the ambituous kind of writer, so I want feedback on every aspect of the story. Other writers don't want feedback on grammer and spelling, possibly because they're ESL or dyslexic or very young. Others again don't really care about the world, seeing it as merely a stage for their plot; since I'm very intersted in worlds, and tend to want te story to answers my questions about the world, I'd be a bad match for that specific kind of writer. (Note that "I want feedback on everything" is a good indicator of ambition level; of being headed in the direction of gatekeeperland.)