The Argonauts were kind of the ancient mythic version of the Justice League/Society, a collection of all the big heroes and doers of deeds of the day. A lot of the Argonauts were also in other big crossover events of the time, like the Calydonian Boar Hunt and the Trojan War. To help you understand them, I thought I'd explain in terms of the heroes we read about today.
By the way, if all those movies about the Argonauts had used some of the cool powers the original gang had, they would have been a lot more interesting, kind of like Heroes with nothing but oily dark-haired men in scanty costumes... !
Nestor was a tedious old windbag who was about 110, and was full of unwanted advice and lectures about how much better people were in the old days. Whenever Nestor opened his mouth, that's pretty much the readers clue to kick back and put your feet up, and pretend your visiting you're grandfather. For Nestor, read ALAN SCOTT.
Zetes and Calais were brothers. They actually had wings and could fly, because of their crazy origin of being the kids of the King of the Winds, Boreas. They were also really horny devils, because they were always pestering Hylas, the group's pretty boy. So, despite the gender difference think of them as HAWKMAN and HAWKGIRL.
Herakles I'm sure you already know; big strong man. Ordinarily, I'd want to associate Herakles with Superman, the JLA's strong man. But Herakles was generally portrayed as bone stupid. Therefore, for Herakles imagine HAL JORDAN.
Herakles had a little sidekick (lover, really), his cousin, Hylas. Hylas was a total pretty boy and always getting in trouble because of it. For Hylas, imagine KYLE RAYNER.
Okay, seriously, Herakles was so powerful that he actually created story-telling problems (since he could pretty much single-handedly beat the snot out of anyone the Argonauts encountered). In that sense, he is very very much SUPERMAN.
Odysseus was the Smart One. Oh, sure, he could fight, but he preferred to use his wiles and wits. He also had a really popular stand alone book of his own, where he fought lots of bizarre enemies. For Odysseus, picture BATMAN.
Philoctetes was a master bowman whose feet stank. Nobody could stand him, so the other heroes marooned him on an island. For Philoctetes, read GREEN ARROW.
Tiphys was the original master helmsman of the Argonauts ship, but he died mysteriously and was replaced by Ancaeus, another helmsman who had little use for religion or prophecy. For Tiphys and Ancaeus, I choose the original and the new MISTER TERRIFIC.
Atalanta. Well, she was strong and fast. And the only woman. That pretty much makes her WONDER WOMAN, by default.
Argus was the builder, the designer; he made their ship, modestly naming it the Argo. That would have to be JOHN STEWART, I guess, since he's the only architect/designer in the entire DCUniverse.
Butes was a great lover, a king, and a bee keeper. So even though he was more of a queen, we give this one to THE RED BEE.
Euphemus could walk on water ... literally. That's because he was the son of Poseidon, god of the sea. So Euphemus kind of has to be AQUAMAN.
Autolycus (yeah, like the guy on Xena, *sigh*) was a master thief and infiltrator. So to me that's got to be the quiet and sneaky MARTIAN MANHUNTER.
Orpheus is remembered mostly as a musician, but he practiced medicine, augury, and the magical arts. He was a magical utility tool, so we name him DR. FATE.
Medea was a trampy, vicious, witch. No contest: ZATANNA.
Iphiclus was a very fast runner and had trouble with impotence. Yes, really. Let Iphiclus be THE FLASH.
Aethalides; cool guy. He was the son of Hermes from whom he received the gift of total recall. Ironic that some one who could forget nothing is no longer remembered. He was the herald of the Argonauts. Let's term him ORACLE.
Bellerophon. Well, he did lots of cool stuff, but really he's remembered because of his flying horse, Pegasus, so THE SHINING KNIGHT is not a bad way to think of him.
Oh, you thought Perseus had Pergasus? No, that's a Renaissance add-on to his myth, perpetuated by Harry Hamlin. Don't believe everything you see in the movies, folks. Perseus had no natural superpowers, but was really smart and had a knack for picking up superpowerful objects and using them to kill crazy monsters and villains. Let's think of him as THE GOLDEN AGE STARMAN.
Poriclymenus had the superpower of shape-shifting into different animals. No, I'm not making this stuff up. Poriclymenus is BEAST BOY.
Lynceus had supersight, even X-ray vision. Not much more too him than that, and the closest thing I can come up with is DR. MID-NIGHT.
Jason was a very accomplished, naturally noble youth who tended to sleep with people he shouldn't. Let's just call him NIGHTWING, for short.
Polydeuces had a lot of relationships with Big People in Big Myths. But we don't care about that. Polydeuces was a great boxer, having defeated the great boxer and demigod Amycus. So Polydeuces can be WILDCAT.
There are lots of more Argonauts-- around 50 total -- but many of those are colorless also-rans.
We call them GEO-FORCE.