You can't tell the players without a scorecard, right? Here are (most of) the members of the Silver Age Superman Family as they appeared on the back cover of Superman Annual #6, Winter 1962-1963:
1. Jonathan and Martha Kent. Superman's adoptive parents had been around since the late 1940s, appearing in the Superboy stories only. The Kents were initially farmers, but in the Superboy series at the time they were now proprietors of a general store (a smaller forerunner of today's supermarket). They had passed away shortly before Clark moved to Metropolis to pursue his career.
2. Krypto. Krypto had been baby Kal-El's pet on Krypton, who made it to Earth in a test rocket of Jor-El's. His first appearance was in Adventure #210 (July 1955).
3. Streaky, the Supercat. Streaky was a earthly pet of Supergirl's who gained superpowers when exposed to X-Kryptonite, a product of an experiment by Supergirl in an attempt to cure her weakness to Green Kryptonite.
4. Comet, the Superhorse. Comet was originally a centaur who first appeared in Action #292 (October 1962). Circe, a female magician, attempted to turn him into a man, but the spell backfired and he became a horse. As compensation, Circe gave him superpowers. When an actual comet entered the solar system, he would be briefly transformed into a human being, in which form he became one of Supergirl's many boyfriends.
5. Mr Mxyzptlk. Pronounced Mix-yez-pit-el-ik. He was a fifth dimensional imp and prankster. Although very annoying, he was not a villain per se, being more of a pest. He could be forced to return to his own dimension for three months by being tricked into saying his name backwards. He had many appearances in the Golden Age as Mr Mxyztplk, but he had been defunct for several years before returning in Superman #131 (August 1959).
6. The Legion of Superheroes. A team of crime-fighters and do-gooders from the 30th Century who first appeared in Adventure #247 (April 1958). The characters pictured here are Sun Boy, Cosmic Boy, Lightning Lad, Saturn Girl and Chameleon Boy. The group included many other members, with Superboy and Supergirl each joining during the Silver Age.
7. Jor-El and Lara. Superman's parents from Krypton. Although dead for many years, they made frequent appearances in the Silver Age through time travel, imaginary stories and devices that could capture the past. Jor-El, in particular, became a very significant character during this era.
8. Lori Lemaris. Lori is "The Girl in Superman's Past", Clark Kent's college sweetheart in a wheelchair, who turned out to be a mermaid from Atlantis. First appearing in Superman #129, (May 1959), Lori refused a marriage proposal from Clark, but they remained good friends, and she was one of the few people on Earth to know his secret identity.
9. Bizarro #1. Bizarro was a poor copy of Superman created by a ray machine, who did everything wrong. The first Bizarro perished at the end of Superboy #68 (October 1958). A later version was created by Luthor in Action #254 (July 1959). By this time, Bizarro lived on his own square world called Htrae. Bizarro #1 was the original Bizarro, but there were many others by this time, hence the little medallion designating him as the original copy.
10. Professor Potter. The professor was the catalyst for many silly Jimmy Olsen and Lois Lane stories. He was forever inventing gadgets which would kick-start the story, and initially appeared in Superman's Pal, Jimmy Olsen #22 (August 1957).
11. Superman and Supergirl. The stars of the show. Superman first appeared in Action Comics #1 (June 1938), while Supergirl showed up in Action #252 (May 1959).
12. Lana Lang. Clark Kent's neighbor in childhood, Lana was a frequent pest for Superboy, forever suspicious of his secret identity. Although she had been a longtime character in Superboy as a teen, she made her first appearance as an adult in Showcase #9, in yet another story entitled, "The Girl in Superman's Past." Lois and Lana were (usually) friendly rivals for Superman's affections. Lana worked as a TV reporter in Metropolis. (Kudos to commenter Paul Saether for the correction on Lana's first appearance).
13. Lois Lane. Superman's main girlfriend in the Silver Age, she was also Clark Kent's competitor at the Daily Planet. She had been around since Action Comics #1, marking her as tied for the longest-running character in the DC universe, with her boyfriend. Lois had a few tryout appearances in Showcase during 1957 and was awarded her own book in March 1958.
14. Perry White. The editor of the Daily Planet, Perry was the boss of Clark, Lois and Jimmy Olsen. Usually portrayed as hot-headed, Perry also had a heart of gold. Perry had been around since the Golden Age, although he actually debuted on the Superman radio series.
15. Lucy Lane. Lois' younger sister was Jimmy Olsen's more-or-less steady girlfriend, although neither of them hesitated to date others on the side. Lucy first appeared as an airline stewardess (they weren't called flight attendants back then) in Superman's Pal, Jimmy Olsen #37 (April 1959).
16. Jimmy Olsen. Like Perry White, Jimmy Olsen had debuted on the radio show and then moved over to the comics. He had been a very minor character in the comics before getting his own book in September-October 1954, and the prominence of the character in the radio and TV series were probably the cause of him receiving his own book before Lois Lane.
17. Beppo, the Supermonkey. The final member of the supermenagerie, Beppo was a Kryptonian monkey who had stowed away in the rocket in which Jor-El sent Kal-El to Earth. First appearing in Superboy #76 (October 1959), he was an infrequent character in the DC Universe.
Not shown:
Pete Ross. As I have discussed in the past, Pete was the first character to discover Superboy's real identity chronologically. Pete first appeared in Superboy #86 (January 1961)
Bottle City of Kandor. Kandor was the capital of Krypton before it was shrunk and placed in a bottle by Brainiac. Kandor became a frequent setting for Superman stories after he rescued it in Action #242 (July 1958). I have a long post on Kandor coming up.
Lex Luthor. Luthor was one of Superman's oldest foes from the Golden Age, and the only villain who appeared more or less continously from the 1940s onward. One of the real treats of the Silver Age Superman was the evolution of Luthor's character from that of a standard mad scientist into a complex character. I discussed Luthor's changes in the Silver Age here.
Phantom Zone criminals. The Phantom Zone was first mentioned in Adventure #283 (April 1961). It was a "twilight dimension" where Kryptonians who had violated the law were sentenced. While there they had no physical presence or any ability to interact with the real world other than to talk to people who were telepathic. Ironically, being in the Phantom Zone turned out to be a blessing for the criminals, since they survived the end of their planet. Periodically one of them would escape, causing havoc for Superman. Also, Superboy used the Phantom Zone to save Mon-El, who was dying of lead poisoning at the time.
Fred and Edna Danvers. The Danvers adopted Linda Lee (Supergirl) a few years after her arrival on Earth and learned her real identity.
Zor-El and Alura. Supergirl's natural parents, they were thought to have perished with Argo City, but they beamed themselves into the Survival Zone, an alternate Phantom Zone. Eventually Supergirl rescued them, and they lived in Kandor.