It's a tricky balance preparing to write for a short story.
I've veered between two extremes. On one hand I enjoy creating page after page of back story for characters even if I know they'll never actually make it into a story. I've created family trees to the third generation, elaborate maps of fictional neighborhoods and timelines spanning centuries.
On the other, I've always had the ideal that short stories just sort of happen. That a good story is a singular moment of creation stemming from some profound and mysterious process deep within the human mind. A story isn't written, it's summoned. Planning, preparation, brainstorming were all harmful to the ritual of the thing. The more I set down ahead of time the more possibilities I was closing off permanently before I even gave the story a chance to work itself into existence.
Then I decided I wanted my stories to be read by a general audience and I realized that neither the 'labor of love' or the 'throw it together on a run' model quite works.
Stories are not so much singular moments as they are the product of a process. They are an endeavor and require certain preparations. But, also, it's tough to have an adventure in a story shrink-wrapped and precisely labeled. My current ideal is to set up characters that reveal themselves through the story. I have to know who they are, but I also have to predict who they might become. The trick of writing a short story is introducing complicated people to complete strangers, I need to show who these characters are in such a way that readers feel like they know how they are going to act. There are people I work with every day I'm not sure I could do that with.
I have to set up their world. That's true for speculative fiction, but it's true for even more conventional 'realistic' fiction. Every character occupies a certain fiction space, a narrative time. For a short story it's not possible to set down every single detail about that world or desirable. I think I can set up some good scenery though. I can create a few impressions that the reader fills in with memories and associations. I might not know exactly what is inside every house that a character walks next to on the way back home, but I want the reader to be able to guess.
I think what I'm describing then is less a list of details and facts than a process that could generate consistent details and facts. It's almost like one of those randomizer webpages that will spit out fake names, places and spy movie plots. I know I've done my homework if I'm able to take two characters, put them in a room together and improvise a scene consistent with the rest of the story.
For characters I begin by setting them up like a character in an RPG. I give them a backstory, focusing in on a moment (off-screen) that really served to bring them to the beginning of the story. I use the characters to sketch out the world. I think about how the character might actually function in the story. What are they likely to say. What sets them off. I think of these things almost like tags or key words. There is more to the character than what I write down but for a moment in time described in 2,000 to 7,000 words, this suffices.
I sketch out the plot as well, again, not in much detail but enough to for me to see where all the pieces are going. I work backwards, which is a trick I learned from a writing class and from designing lessons as a teacher; I know where I want to be at the end and then just trace how to get there through the proceeding pages.
Then I clear the deck and let myself write. I can't claim any success with any of this, but maybe the process that's I've described strikes a chord with you.