If you are wondering what stories to read, you might want to take a look at this list of popular anthologized short stories prepared for Literary Hub: http://lithub.com/the-most-anthologized-short-stories-of-all-time/. I was pleased that some of my favourites made the list: “The Lottery” by Shirley Jackson; “Eveline” by James Joyce; “The Doll’s House” by Katherine Mansfield.
If you are looking for some of these stories and don’t have any anthologies at hand, check out https://americanliterature.com/short-story-library. They have thousands of titles which you can read on the spot.
Here are a dozen stories which did not make the above list but which I used with my students in the past and which I think serve as a great introduction to the genre (an * indicates the author is Canadian):
“By the Waters of Babylon” by Stephen Vincent Benét
“A Sound of Thunder” by Ray Bradbury
“The Pedestrian” by Ray Bradbury
“All the Years of Her Life” by Morley Callaghan*
“The Two Fishermen” by Morley Callaghan*
“The Last Leaf” by O. Henry
“The Monkey’s Paw” by W. W. Jacobs
“Horses of the Night” by Margaret Laurence*
“The Interlopers” by Saki (H. H. Munro)
“Laura” by Saki
“The Lamp at Noon” by Sinclair Ross*
“One’s a Heifer” by Sinclair Ross*
If you are really pressed for time, why not read some micro-fiction. http://lithub.com/11-very-short-stories-you-must-read-immediately/ takes you to a site where you can read some very, very short stories.