I've posted on about half the Leinster stories I've read so far; here is a selection of some good ones from among those posted.
He's generally a reliable author. I've read dozens of his stories, including some novels, & I don't think many were disappointing. Some of his stories, however, are more thoughtful than others which are more of adventures.
- "First Contact" (download text scans as part of Astounding issue it originally appeared in, or as MP3 of a radio adaptation): Probably his most famous story - the one that coined the term "first contact" in modern sense. This is a story about establishing trust among strangers, where the cost of a breach of trust are unacceptably high. His solution is not really applicable to the problem of trust among the strangers on internet, but I liked the story.
- "The Aliens" (download text, or two part audio): Similar situation as "First Contact", but a less famous story. Circumstances ensure that the murderous first contact between humans & aliens has a peaceful outcome.
- Medship series of stories (download) are consistently good - a young medic/diplomat solves a major problem in a society in each story. My personal favorites are "The Grandfathers' War" (download) & "The Mutant Weapon" (download), but most others are good too. Former is an intensely emotional story about a tragedy that actually happens in a lot of families, later is one of the better thrillers on colonizing by spreading a plague to which colonizers are immune.
- "Dear Charles" (download) is one of the coolest & hilarious reads on grandfather paradox.
- "The Swamp Was Upside Down" (download) is very interesting read on landslides, one of his few hard sf stories.
- "A Logic Names Joe" (download text/radio adaptation) is a very funny classic that gets a lot right about social implications of modern computers & internet - something very rare for a 60 year old story, written when even the modern terms about computers were yet to be invented.
- "The Mad Planet" (download) is one of his most famous stories - a post-apocalypse story that's actually about a fun adventure on a curious world.
- "Solar Constant" (download) is one of the more interesting terraforming stories by anyone.
- "Sidewise in Time": One of his most famous stories - the story that invented parallel universe & alternate history subgenres. I personally didn't like it much though, & have a feeling US readers might like it more than others.
- "The Ethical Equations" is not only a good read, but is probably important in that it led to Arthur Clarke's very famous novel "Rendezvous with Rama" via Clarke's own "Jupiter Five". "Jupiter Five" is practically a rehash of "The Ethical Equations". Story is of a ... sort of, but not quite ... first contact with alien visitors to Sol. It's online somewhere, but I don't have the URL handy.
- "The Lonely Planet" is a very curious story of a sentient world, treated by humans as they would treat a draft animal! Adventure follows the human discovery that the animal is far smarter than them.
- "Proxima Centauri" is one of the best bug-eyed monster stories, though I found the ending less interesting than rest of it. Human visitors to Proxima Centauri are treated by local intelligent plant beings the way we treat vegetation! It's online, but I don't have the URL handy.
- "The Strange Case of John Kingman" is one of the rare low-key stories of Leinster. No great adventure - just the observations about a very curious inmate of ... was it a lunatic asylum? I don't quite recollect the place. I think this is online, but I don't have the URL.
- "Sam, This is You" (download text/audio): While this is not quite in the class of stories above, I note it because 2010 Hindi movie "Karthik Calling Karthik" (@IMDB) had exactly this idea.
- "The Runaway Skyscraper" (download) is his first science fiction story (I think). Nowhere in the class of stories above, but may be of particular interest to residents of New York city. Adventure of people inside a building in modern New York in the world that existed at their geographical location some centuries back, when a variant of an earthquake "sank" their building in time rather than space!