Reddit mentions of The Best of the Best

As a new reader of SF, I'd recommend some of the 'Golden Age' authors. The easiest and cheapest way IMO is to start with an anthology, such as The SFWA Grand Masters series. This would expose you to many authors from which to expand your library. If looking for something newer, there are many contemporary 'Best Of' anthologies of novellas and short stories that you could wade through. The benefit here is that you get exposed to many authors quickly as each is a quicker read.

Examples: https://www.amazon.com/gp/bookseries/B0163I5PQG/ref=dp_st_0312868804

https://www.amazon.com/Best-20-Years-Science-Fiction/dp/031233656X/

https://www.amazon.com/Modern-Classic-Novels-Science-Fiction-ebook/dp/B00NKBSID2

Frederic Brown was a master of the short story. Look for his story "Knock" online. It will tell you if you will like his work.

Gardner Dozois, who recently passed, publish a yearly anthology of the best short stories and novellas. You might check out his "Best of the Best".

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I personally like Jack McDevitt's "Cryptic".

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For the stage I would think you'd want something that emphasizes psychology or hard science or character development since FX aren't as practical, so I'd say "A Dry, Quiet War" by Tony Daniel, which appears in the anthology Best of the Best: 20 Years of the Year's Best Science Fiction.

It's a cool story about a soldier from a war literally at the end of time, who comes back after the war to his original wild-west style town, hooks up with an old flame, and also happens upon some unsavory other characters from that same war whom he has to battle. It has some interesting character development and tension which might be well-conveyed on the stage.

You can find anthologies of short stories, which I think are great. This is one of my favorites. Has such a wide range of short stories, it might help you find what settings and themes you like more than others.