I also want it to be something that can be easily related to modern life and easy to understand.
"A Rose for Emily" by William Faulkner is a great story with obvious themes and an interesting structure. Stories by Nathaniel Hawthorne also have obvious themes and the allegory of some like "Young Goodman Brown" also help with understanding the intended meaning of the work.
You may have already read this one, but "The Lady or the Tiger?" is a short story with several rather clear-cut themes. Another is "The Interlopers" by Saki (H.H. Munro), and "The Fifty-first Dragon" by Heywood Brown would be a bit lighter reading with a clear theme, as well. You have a great list here. Happy reading!
"Two Kinds" by Amy Tan
"The Yellow Wallpaper" by Charlotte Gilman Perkins
"The Gift of the Magi" O. Henry
One short story that you could try is The Story of an Hour by Kate Chopin. It is incredibly short, easy to understand, and has a strong theme of marriage and the roles we play within it. I provided a link to it below.
Any of O. Henry's short stories are very easy reads, and are super entertaining. The one with the strongest theme is probably Gift of the Magi, which talks about sacrifice and love. I provided a link to a good number of his stories, and hopefully there is at least one in there that will work for you.
One last suggestion is The Necklace by Guy de Maupassant. This has powerful, almost overtly stated themes of pride, vanity and materialism, and how they lead to the downfall of a woman. I provided a link below with the text and commentary. I hope that those work for you, and good luck!
One other story with a timeless theme is "The Piece of Yarn" by Guy de Maupassant. The author's intense examination of the inner workings of the mind is intriguing and the theme of deceit leading to more deceit and then defeat is relevant to audiences today.
Another tale, one of true adventure and danger, is The Open Boat by Stephen Crane. This story is based upon a real incident in which Crane and two other men were stranded in a small boat for thirty hours. It is a tale of man vs. nature, of course--one that usually appeals to male readers, especially since it is based upon reality.
Hope these help!
the landlady and lamb to the slaughter by Roald Dahl
A story you might not know:
On The Sidewalk Bleeding by Evan Hunter
It has obvious themes like death, individual vs. society...
Anthem, by Ayn Rand, is very short with a very obvious theme. It is easy to do a compare/contrast to modern life.
Bjornstjerne Bjornston: The Father
Ernest Hemingway: A Day's Wait