A Greek hero is more than a just a sum of their advantages. To turn the bones of the character into a living legend their story must be fleshed out.
The polis a person grew up in or is loyal to is an important part of their character. Each city has a subtly different outlook on life and preferences for different gods, with some cities having strong ties to a single patron god. To all Greeks, service to their polis is how a person gains glory and this doesn't change when a character becomes a champion. Characters can expect to be especially lauded and praised in their home polis but in return they are expected to support and assist the polis' goals and ambitions. The inevitable clash between the needs of their polis and the needs of the hero's patron deity is just part of a champion's life.
Neither Hades nor Hestia are associated with specific locations. Both gods have realms (death and the hearth) which are central parts of Greek life and their worship is on a smaller scale but far practiced universally.
Social status is very important in Greek society. From top to bottom the strata of social status are aristocracy, citizens, commoners, foreigners and, at the bottom, slaves. The aristocracy come from families with wealth and power, whether the polis is democratic or otherwise. Citizens are property owners and important members of the polis with greater freedom in exchange for greater responsibilities. The commoners and the foreigners lack the right to own property and have no influence in the city's politics but are otherwise free to be as poor or rich as they wish. Slaves are the property of their owners and are limited to as much freedom as their owner grants them.
As champions of the gods, the player characters are prominent and respected individuals. While most Greeks will treat them with deference, a few with power, wealth and conviction will see things differently. No one will risk the anger of a god by obviously insulting a champion but there are many subtle ways for the high-born to snub the low-born. Conversely, being low born may open doors and loosen tongues among those who fear the higher reaches of society.
What was the character's life like before becoming a champion? Who did they live with, who did they love and how did they earn a living? A mortal's life is shaped by these questions and the answers speak volumes about the character's personality. Players should consider how being chosen changed the character's life. Champions receive no payment from their patron (though they can expect help in extremis from the god's temples) so they must still support themselves and their loved ones.
The gods select champions who have both the skills they need and a similar personality to their own. Players should consider carefully why the god chose their character to be a champion. Which skills does the god value and what type of behaviour does the god expect from the character?
Every champion has a moment when they ceased to be an ordinary mortal and became a hero. How this happened is unique to each champion. It ranges from a direct encounter with their god, possibly undergoing a series of trials to prove their worth, to simply waking up one morning knowing they are now the personal servant to a deity.
The player should consider how the character was selected and the character's reaction to it. Some people are born heroes, others have heroism thrust upon them.
Every hero needs a name. There are many lists of Greek names available on the internet and players are encouraged to select one they can pronounce. Greeks tend to only have a first name and are known by their polis, for example Xeros of Athens.