The first is The Complete Stories of J. G. Ballard. Ballard is probably most famous in America as author of Crash, the novel the movie, and now TV series were based on, but he is a major force in late 20th century English Literature. His work is so distinctive and influential that you can now describe something as "Ballardian." The Complete Stories of J.G. Ballard is a great opportunity to get a feel for this complex and prolific writer.
The second is The Collected Stories of Lydia Davis. Davis is one of the most innovative and vibrant short story writers in America, and one of my personal favorites. Her stories have an edge of intellectualism, humor, and surrealism that too many writers fearfully avoid. She was writing flash or microfiction before there was a name for it. For example, here is her "story," "Samuel Johnson is Indignant:"
that Scotland has so few trees."We Miss You: A Study of Get-Well Letters from a Class of Fourth-Graders," from her National Book Award Finalist Varieties of Disturbance, is one of my favorite short stories.