To most of us kids, it seemed as if Brainiac was like Luthor; one of those villains who'd always been around. It wasn't until later that I learned that he actually had originated in July of 1958, and thus was only a little over a year older than Supergirl, in comics time anyway.
His first appearance, in Action #242, is also famous for introducing the bottle city of Kandor, an enduring plot device for the rest of the Silver Age. Here's how his passion for reducing cities was explained in that issue:
Superman managed to escape, and restore the Earth cities to their normal size. But when there was only one charge of the enlarging ray left, he was left with a moral dilemma; should he restore himself, or Kandor. Fortunately for us, a rocket ship from Kandor, piloted by Jor-El's old college roommate made the decision, pressing the button to return Superman to his normal size. Brainiac is under sedation for the 100+ year trip back to his home planet.
He returns in Action #275. In that story, he beams Superman with a combination red and green Kryptonite ray, which mostly impacts Supes like ordinary Red K. He grows a third eye in the back of his head, which comes in handy as with three eyes shooting heat vision at Brainiac, he is able to dissolve the villain's force field. He sends Brainiac back into the past on some remote planet, reasoning that this will get him out of his hair for awhile anyway.
Excluding the oddball Night of March 31st story which I covered years ago, Brainiac's next appearance came just five issues later:
His next significant appearance (Brainiac often appeared in cameo flashbacks whenever the Bottle City of Kandor was mentioned) was in Action #286, when he teamed up with some other villains:
His "next" appearance is actually chronologically one of his first. See, some of Brainiac's henchmen kidnap little Kal-El on Krypton and bring him to Brainiac's home planet, given a name for the first time:
In Brainiac's next appearance, a startling new fact was learned about him: he is a computer!
Armed with this knowledge, Luthor decides to free Brainiac from the prison planet where he's locked up, and to improve the computer:
Brainiac and Luthor team up to rob Superman of his powers and shrink him to the size of a small bird. But while they're bickering over who gets to kill him, Superman escapes and sends a message to the Superman Emergency Squad in Kandor. They arrive and make short work of the villains, but in the meantime, Brainiac has put Supes into a coma, from which the finest Kandorian scientists cannot rouse him. Brainiac makes a deal; if Kandor lets him and Luthor go, he will release Superman from the coma. Oh, and along the way, he hypnotizes Luthor into removing the secret timer, and forgetting about Brainiac being a computer.
After that, Brainiac pretty much becomes Superman's generic villain from space. Oh, occasionally we hear about his twelfth-order computer brain, or his hatred for Kandor, but there's no real attempt to fill in the holes in the back story of Bryak, although I assume a lot of that has chanced since the end of the Silver Age.