score:5
To answer your immediate question, the sarcophagus would have been for a wealthy Roman. In the case of the Genzano sarcophagus you cite, like many similar ones, the name of the deceased is unknown.
During the high Imperial period of Rome, 200-400 A.D., sarcophagi such as these were popular. They were often decorated in high relief and contained mythological scenes, often involving death or the underworld. The Labors of Hercules was a popular theme. Note that the last of the labors was to retrieve the hound of hell, Cerebus, and bring him out of Hades. Another common theme was Hercules rescuing Alcestis from Hades. The myth of Persephone, who was kidnapped by Pluto and became the queen of Hades, was an extremely popular theme for sarcophagi.
The style you saw at Antalya, shown in the photo above, is typical, with a temple-like roof and high-relief panels separated by Corinthian columns.
Some moderns may find it a little odd to have superhero mythology on a burial container--sort of the equivalent of having Batman comics on your coffin--but for the later Romans such things were common. They also decorated their houses with exactly the same kinds of art: Hercules, myths, scenes from the gods, and so on.
There was a professor at Barnard named Marion Lawrence who devoted her career to studying classical sarcophagi and you can research the topic by reading her papers.