Reddit mentions of The Collected Stories (Gollancz)

I would absolutely recommend this as a primer for the genre.

Although it's only the one author, Clarke was instrumental in codifying science fiction into the viable genre it has become today and in this set of stories we can see the emergence of so many of the themes that later became synonymous with science fiction as a whole. You can also watch the evolution of the ideas that eventually became 2001 A Space Odessey develop, (imo he wrote that story about 50 times in different settings.)

It's definitely one of the books that introduced me to the genre. I'm also a big fan of his Tales from the White Hart collection (although I think these are included in the other book.) They have a more humourous outlook on the subject.

I'd also recommend Aliens For Neighbours by Clifford Simak as well as any Bradbury, Asimov or Dick.