The Untold Secret History of  the

The official beginning of the history of the Phantom Zone is in Adventure Comics 283 from April 1961.  However, like many other Mort Weisinger-edited stories of this era, it combined elements and recycled ideas from previous stories going back over a decade. So let's start at the beginning and go backwards, shall we? 
"The Phantom Superboy"  by Robert Bernstein and George Papp.
Adventure 283. The first weapon turns out to be a disintegrator ray, the second is an enlarger.  The third is a strange helmet which Superboy puts on. The helmet projects thought images directly into the brain of the wearer, so Superboy actually sees the history of the Phantom Zone. 
Still, he accidentally gets trapped there and can only be rescued when he uses his super-thoughts to project a message into Pa Kent's electric typewriter.
Forbidden weapons from Krypton?  Where have we heard that before?  In February 1952 in Superman 74, Ed Hamilton,  Wayne Boring and Stan Kaye introduced a bunch of forbidden weapons from Krypton, built by Jor-El and launched into space in a giant green crystal (hm...), one of which was an invisibility spray.
Anybody who'd been reading comics for a little while in 1961 might've noticed an eerie resemblance between the "Phantom Superboy" and a tale published only a couple of years earlier called "The Ghost of Lois Lane!" (Superman 129, May 1959, by Jerry Coleman, Wayne Boring, and Stan Kaye).   Prof. Grail's Space teleportation machine is accidentally activated by Superman. He's thinks he's killed Lois, but all he's done is project her into the fourth dimension...
Readers who had been around a little longer than that even might have remembered Jimmy Olsen #12 back in April, 1956.  Doc Brane is one of  Jimmy's coterie of crackpot inventors. In hopes of a scoop, Jimmy volunteers to test the Doc's 4th dimensional transporter, only to discover there's no way to get back.  Unless you own a typewriter...
But wait, there's more!  In 1950, the movie serial "Superman vs. the Atom Man" featured a sequence in which Luthor teleported Superman into another dimension he called "The Empty Doom".  Superman sent a message to Lois Lane via an electric typewriter which told her how to rescue him.
Writers George Plympton and Royal Cole apparently got the
idea from a recent Action Comics (#131, April 1949) in which Luthor used a ray to transport Superman into the fourth dimension.  The story, "The Scrambled Superman"was written by Joe Samachson and drawn by Al Plastino. 
Superman used the same electric typewriter gimmick to tell Lois Lane how to rescue him from his disembodied state.  When editor Mort Weisinger found a gimmick he liked he used it over and over (and over and over).
The concept goes back even further than that, however.  In his  Jan1942 story "Adventure on Poloda" (Beyond the Farthest Star), (Blue Book Magazine) Edgar Rice Burroughs used the thought powered typewriter to explain how he learned of the adventures of his interstellar traveling hero.  I can't swear this is the first time the idea was used.  It's probably as old as electric typewriters themselves.
The first Phantom Zone story introduced two villains. Even though they were quickly dispatched within one page. Dr. Xadu was condemned for experiments with suspended animation.  Then there was the case of General Zod, who created an army of bizarro duplicates of himself with which to take over Krypton.  An actual fight with Kryptonian villains was promised for an issue of Superman. Two months June 61 later in Superboy 89, the Boy of Steel had to retrieve that Phantom Zone projector.  His friend, Mon-El was dying from lead poisoning and only being projected into the Phantom Zone would keep him alive long enough for Superboy to discover a cure.  "I'll free you someday when I grow up to be Superman! I swear it!" The caption reads "watch Superman comics for a 3-part novel featuring Superman's return to the Phantom Zone!"

Mon-El was  rescued from the Phantom Zone by Brainiac 5 in Adventure  #305. So why was Superman still trying to come up with a way to free Mon-El when he knew that he would never succeed and Mon-El would be stuck in the Zone for a thousand years?  Time travel is soooo confusing.

But September 1961 brought the next appearance of the Phantom Zone- and it was still in Adventure.  An evil youth from Krypton named Dev-Em who plotted his own escape from the planet using Jor-El's stolen notebooks, projected Superboy into the Phantom
Zone, using a punishment ray he'd stolen back on Krypton.  This time Superboy is forced to watch the evil Dev-Em masquerade as him, performing evil deeds to ruin Superboy's reputation.  Still no Kryptonian villains, however.  But the letters page touted that
Superman three-parter again. by Jerry Siegel and George Papp. Adventure 288.
Bernstein got control of his own idea back in the next issue, featuring "Clark Kent's Super Father" with art by George Papp. Jax-Ur escapes from the Phantom Zone and masquerades as Dad Kent, trying to drive Superboy crazy by pretending Dad Kent has super-powers.

Jax-Ur was imprisoned in the Phantom Zone for blowing up one of Krypton's inhabited moons. (although in this version, he didn't do it on purpose.)  He had escaped from the Phantom Zone through a temporary warp created by a passing comet.

Bernstein's  great cosmic confrontation between Superman and the Phantom Zone villains finally arrived in Action Comics 284  and featured this dramatic cover. "We defy you to guess the reason why the mighty Superman transforms himself into the Babe of Steel!" read the January 1962 cover blurb.  The cover illustration of Superbaby hammering the police chief's desk with his super-fist must have made quite an impression on Mort Weisinger the first time it was used back in Superman 66 by William Woolfolk and Wayne Boring.  (Itself based on a 1948 Sunday newspaper sequence by Alvin Schwartz and Wayne Boring).
Superman deliberately reduces himself to the size of an infant by exposing himself to a piece of Red Kryptonite he had lying around for just such an emergency and then spends most of the story just doing regular super feats. 

Finally  Super"baby" reaches the Aurora Borealis and finds a hole in it which goes into the Phantom Zone.  With his new super-small body he canpass through the hole and into the Zone itself.  There he meets Jax-Ur and Professor Vakox (whose mad experiments filled Great Krypton Lake with sea monsters) and Mon-El- still trapped there. Then, Superman, Supergirl and Krypto reseal the hole and all is well.

In May 1962, the Zoners returned as three of them combined their mental powers to force Supergirl's foster father to open a portal to the Zone so they could escape. Jax-Ur, Vakox, and Xadu appear, along with Mon-El. (Dorfman and Mooney)  Even though outnumbered three to two, Mon-El and Supergirl defeat the Zoners without throwing a punch. Action 288- "The Man Who Made Supergirl Cry"
Elastic Lad Jimmy Olsen wormed through a tiny hole into the Phantom Zone in issue 62 of his own book.  There Jax-Ur, Xadu and Vakox tried to get him to learn Superman's secret identity. (July 1962- Leo Dorfman, Curt Swan and George Klein) Erndine Ze-Da Superboy 100 Siegel and Swan.  Teamed with Xadu, she tried to drive Superboy crazy by pretending to be Martha Kent pretending to be Lara.  Oct 1962.  Interestingly, she and Xadu were not returned to the Phantom Zone at the end of this story but were left stranded on an alien planet. The only named female Zoner introduced in the 1960's.
Quex-Ul from Superman 157 was that anomaly, the innocent convict.  Brainwashed into even thinking he himself was guilty, Quex-Ul was the first prisoner ever released from the Phantom Zone for completing his sentence.  By Robert Bernstein, Curt Swan and George Klein November 1962 The true culprit was Rog-Ar, a man who should have been in the Phantom Zone, but instead perished when Krypton exploded. Superman 157. This issue also introduced Gold Kryptonite.
In Action 297 it was revealed that all the Forbidden Weapons (except the Phantom Zone Projector) Superboy found in that box were actually created by Kru-El. (Obviously a relative of some sort.)  Kru-El, Jax-Ur and Zod (making a rare appearance) escape from the Phantom Zone and team up with a super-powered Lex Luthor in Feb 1963. By Dorfman and Mooney. Why was the Phantom Zone projector in that box, anyway?
The answer was revealed in Superboy 104 April, 1963 by Robert Bernstein and George Papp.  Gra-Mo was the last criminal exiled into space before Jor-El invented the Phantom Zone projector.  He didn't end up in the Zone until years later when his plot to take revenge on Superboy failed.  Jor-El invents the Projector as a more humane way to punish prisoners rather than blasting them into space with no hope of return.  But it turns out the Zoners have telepathic powers with which they can influence people on Krypton so the projector is banned.

Tor-An Phantom Zone villains have a different way of taking revenge on Supergirl. They marry her.   Action 307- Leo Dorfman and Jim Mooney.  Dec 1963. Jer-Em was sentenced to the Phantom Zone after Krypton was destroyed for crimes committed on Argo City. Action 309 Feb 1964 Jim Mooney.
Superman, ever the humanitarian, commutted the sentences of Phantom Zone prisoners if they repented as did Vorb-Un in Action 310.  March 1964. Jax-Ur took the same opportunity to create Jewel Kryptonite. Ga-Zor Adventure 323 was given the longest sentence of any criminal. He was still in the Zone during the Legion's time, for trying to destroy Krypton with his earthquake machine. by Jerry Siegel and John Forte. August 1964.
Py-Ron Action 323- in a really convoluted plot involving the planet Feminax, home of the Feminaxies, Pyron was released from the Phantom Zone and donned the identity of Evil Man. Leo Dorfman and Jim Mooney  April 1965 Ak Var Action 336 Ed Hamilton, Curt Swan, and George Klein April 1966. Ak Var served his sentence and was released, rehabilitated and eventually became Flamebird, to Van Zee's Nightwing.
Nam Ek Superman 282 Martin Pasko and Ernie Chan  Nam-Ek's adventure appeared in the World of Krypton series.  He sought immortality and was horribly transformed.  How he later got into the Phantom Zone is unknown to me. Faora Hu-Ul Action 471 May 1977 Cary Bates,. Curt Swan, Tex Blaisdell. Created after the first Superman movie made the idea of a female Phantom Zone villain popular and DC realized they didn't actually have one.
Aethyr, the cosmic being whose thoughts create the Phantom Zone, a very un-Silver Agey addition to the mythos by Steve Gerber and Gene Colan- Phantom Zone 3, Mar 1982. Az-Rel  and Nadira- Phantom Zone 1 Steve Gerber, Gene Colan- Phantom Zone 1 January 1982.