I'd recommend 'A Sound of Thunder' by Ray Bradbury. It's about time travel and how a small change in the past can have huge and unexpected consequences in the future. And 'The Star' by Arthur C. Clarke is also very good. It combines science fiction elements with religious and philosophical ideas as it tells the story of a group of astronauts who discover a strange star.
One interesting fantasy sci fi short story is 'Flowers for Algernon' by Daniel Keyes. It tells the story of a man with an intellectual disability who undergoes an experimental procedure to increase his intelligence. It's a very moving and thought - provoking story. Also, 'Harrison Bergeron' by Kurt Vonnegut is a classic. It's set in a dystopian future where everyone is made equal in the most extreme and absurd ways.
Sure. 'The Cold Equations' by Tom Godwin is a great one. It's about a spaceship pilot who has to make a tough decision regarding a stowaway on a mission where every ounce of fuel matters. Another is 'The Veldt' by Ray Bradbury. It shows a future where technology in the home has some terrifying consequences for a family.