Otto Binder and Al Plastino introduce Brainiac, one of Superman’s greatest villains, in Action 242 (July 1958), in a story that also introduces the bottle city of Kandor.
Brainiac looks very different than he does on the cover of the issue, and I have a theory about that,which I will get to later. In this story, he is introduced as an alien, who travels around in his spaceship, shrinking and collecting cities from different worlds. He has a pet of sorts, a white alien monkey-type creature called Koko.
Brainiac shrinks Paris and brings it to his ship, with Superman in hot pursuit. Brainiac puts himself into a suspended animation sleep, as he prepares to travel back to his base. Superman takes advantage of this situation. He finds Brainiac’s collection of bottled cities, and enters the one Brainiac seemed to value above all others. Superman discovers that he is in the city of Kandor, stolen by Brainiac before Krypton exploded. Professor Kimda, who had been the college roommate of Jor-El, serves as Superman’s guide as he explores the city, in which he has no powers. Again, gravity is given as the sole explanation for his abilities.
Not very much is seen of Kandor in this story, nor are any other Kandorians brought into the tale.
Superman returns the various bottled cities to their homeworlds, but as he cannot do that with Kandor, he brings it back to his Fortress. Kimda uses the last re-enlarging charge on Superman, which leaves his own people stuck in their bottle. A nice move, but probably not very popular in Kandor.
Now, as to the cover.
The image of Brainiac is so very different from that in the story, but is the way the character will look in later tales. I have a feeling that the story was written with Brainiac intended to be a one-shot villain. After all, it ends with him heading out into space, not due to awaken for years. But then, they decided that this character deserved to be brought back, that his connection with Kandor was too important to just drop. And the look of Brainiac was improved, and then used on the cover.