Breakdown of the eras by timeline with notes can be viewed here and is printed under the response tables, after everyone's answered I'll probably put them in chronological order.

Era Table
?
Beetnemesis - Late Helladic
Bergioyn - Late Helladic
Darth_Katie - Early to Middle Helladic
Fanatic-Templar
Fox and Ravens - Classical
Gher - Late Helladic
Hobo - Classical
Isaac - Late Helladic
Scott Blademaster - Classical
Stephen - Classical
Ranagrande
Yunalesca - Archaic to Classical


Era Guide
Greek Bronze Age
Early Helladic 2800-2100 BC
Middle Helladic 2100-1550 BC
Late Helladic 1550-1060 BC

As the Trojan war appears in the overlap between Late Helladic and Dark Age, people who fought in the Trojan war may select either, and those who are referenced before it or after it pick accordingly

Ancient Greece - 1200 BC-330 AD
Greek Dark Ages 1200-800 BC
Archaic Greece 800-480 BC
Classical Greece 510 BC to 323 BC (Death of Alexander)
Hellenistic Greece 323-146 BC (Annexation by Rome)
Roman Greece 146 BC-330 AD

Medieval Greece 330 AD+
Byzantine Greece and beyond to Modern, I'm not really expecting anything this late