Hi!

I'm looking to start a Greek mythology inspired campaign, using the Theros book for a majority of the world.

But!  I need some help.  I'd like to make some characters based on some of the greatest heroes from Greek Mythology, specifically the following:

Hercules/Heracles

Atalanta

Deadalus and/or Icarus

Theseus

Perseus

Jason (with or without his argonauts)

The idea is that they were heroes before, a sort of Avengers band of heroes that everyone else could run across in the adventure.

Herc is the only one I have a bit of an idea for, making him into a Leonin barbarian.  Which, hey, forgot to mention, taking some creative liberties with these heroes so they're not all Humans/Aasimars.

Odysseus (of “The Odyssey ” fame.), his buddy Achilles, Achilles mortal enemy Hector... don’t forget Ajax.

Oedipus and Antigone, but they might not fit for your needs, although a younger Oedipus might.

PS-Don’t forget that Hercule (another other name for Hercules) was one of Jason’s Argonauts. 

There's basically only three classes that you can expect most Greek heroes to have: Fighter (Champion or Battle Master only), Rogue, or Barbarian.  Greek heroes as a rule did not use any magic beyond innate gifts from being a son of Zeus (Herakles) or from having magic items that were given to them by the gods.  They definitely didn't have any spellcasting ability themselves.

Monk might work if you reskinned it all a Kevin Sorbo.

I suppose you could do that, but I'd be hard-pressed to name a Greek hero who didn't habitually wear armor and use a shield.  Even Herakles did that.

If you want to take a broader definition of hero, as instead just a mythological figure.
I’d say Circe was a wizard.

The three witches who shared an eye might be wizards or maybe warlocks. But I don’t see them as working with the good guys.

Odysseus I could see as a bard, since he was quite the storyteller. 

Cassandra could be either wizard or cleric, just give them lots of divination spells.

For Perseus, there’s Those Boros legionnaires in the ravinca book that fly on rocs (that you could re-skin as a Pegasus) that might work. 

Acteaon could be a beast master ranger (maybe use the UA one so he doesn’t suck)

Atalanta learned how to fight and hunt as a bear would. could go Barbarian, could go Druid if you want to take that phrase more literally. 

The three witches who shared an eye would definitely be a hag coven.

Quote from Xalthu >>

The three witches who shared an eye might be wizards or maybe warlocks. But I don’t see them as working with the good guys.

 
Are you talking about the fates?

Quote from hollowtpm >>

Quote from Xalthu >>

The three witches who shared an eye might be wizards or maybe warlocks. But I don’t see them as working with the good guys.

 
Are you talking about the fates?

 Nope:

https://en.m.wikipedia.org/wiki/Graeae

No the witches that Perseus tricked; (full disclosure, I had to look their name up) the graeae.

And a hag coven would work well for them, I agree. 

sposta ninja’d me, I see

What about Orpheus? Why doesn't he get any love? He's like the ultra bard of Greek mythology. His songs were so powerful they entranced Hades, the lord of the dead.

Or Odysseus (my personal favorite)? He sailed for years to get back to Ithaca, and lost his entire fleet, be he survived. He escaped the Sirens, Polyphemus the Cyclops, Circe, the land of the dead, Scylla, and the wrath of Poseidon himself.

Orpheus would (obviously) be a bard, and I'd say Odysseus would be a Rogue Mastermind/Swashbuckler, and possibly a bit of bard too.

The monsters wouldn't be that hard. The Hydra is already there. The Nemean Lion is just a lion with immunity to piercing and slashing from nonmagical damage and a CR of 3 or 4. Cyclopses are already there. The Minotaur would need to be empowered a bit, because it's the only Minotaur. Medusa doesn't need any changes. The Sea Serpent that Perseus fights would have to be homebrew, though, as would Scylla and Charybdis. The Sirens could be a slightly modified and reskinned harpies.

Yeah, Odysseus was the first one I listed too.

Thank you all so far.  These are great suggestions!

In general a lot of the Greek heroes are either Fighters, Monks, Barbarians or Bards. I'd say that you should keep most of them human because often the whole point of their heroism and adventures is that they are "mere" humans. Many of them could obviously be Aasimar but I'd vote for humans more often than not. As for the ones you mentioned (I'm doing main class only. Many of them can easily have some levels of Fighter):

Hercules/Heracles: Human Barbarian (his temper got him in trouble quite a few times). Go Bezerker if you want to do the easy route, otherwise go Totem and say that the powers manifest through the foes he's slain. Making him a Leonin would be rather interesting since his most famous trademark is wearing the pelt of the Nemean Lion. Is he wearing the pelt of a fellow Leonin or is maybe "The Nemean Lion" an honorific that you get if you defeat the previous lion? 

Atalanta: Human Ranger, Monster Slayer

Deadalus and/or Icarus: Daedalus is an artificer, Icaros is a commoner. :P

Theseus: Human Kensei Monk with the Observant feat. Many of his deeds are about his athletic endeavours so I'd go with that. Maybe give him the Prodigy feat for expertise in Athletics.

Perseus: Aasimar Monster Slayer

Jason (with or without his argonauts): Mastermind Rogue with the Sailor background.

As for some of the others: 

Odysseus: Human Battle Master Fighter/Mastermind Rogue with the Lucky feat.

Achilles: Human Battle Master fighter.

Bellerephon: Aasimar Paladin with Find greater steed.

I made him a Leonin because of both the Nemean Lion and his nickname of the Lion of Olympus.  Thought it was kind of funny.

Quote from Winterhood >>

I made him a Leonin because of both the Nemean Lion and his nickname of the Lion of Olympus.  Thought it was kind of funny.

 You mean from the Marvel comics? That's a fun reference to throw in there. :D

Quote from Lostwhilefishing >>

Quote from Winterhood >>

I made him a Leonin because of both the Nemean Lion and his nickname of the Lion of Olympus.  Thought it was kind of funny.

 You mean from the Marvel comics? That's a fun reference to throw in there. :D

 Exactly!  Big fan of the over the top Marvel version.  Can't wait to give him a Travis Willingham voice.

Orpheus is the inspiration for the Bard class in my opinion. And like Heracles, he was a member of Jason's Argonauts.

And Jason married Medea, who was basically a Warlock/Cleric.

Are you familiar with Damocles?

Sort of.