Here’s a list of some of the major time periods you will come across when searching for antiquities. The dating is a bit rough, these are just generalizations. You'll find that most antiquities dealers work with artifacts from the Near East and the Mediterranean, however some might also offer antiquities from the Far East, such as China and Japan that are not listed here.
Prehistoric: The Paleolithic and the Neolithic periods; generally stone tools and things of that sort are the things you will find here.
Mesopotamian: ~4,000 - 300BC: The ancient Mesopotamian empires: Sumeria, Babylon, Persia, etc.
Ancient Egyptian. ~4,000-300 BC. Time period of the pharaohs and the pyramids.
Ancient Greek: ~1,000BC-300BC: Ancient Greece, time of Plato, Aristotle, etc., prior to Alexander the Great’s conquest.
Hellenistic. ~300BC -100AD. Time after Alexander the Great, extends across the Mediterranean, the Middle East, Egypt and Asia to the border of India
Roman: ~100BC-500AD: Generally refers to the Roman Empire, from about the time of Julius Caesar until the fall of the Roman Empire in the 5th Century AD
Byzantine: ~500AD-1500AD: The Byzantine Empire was the eastern half of the Roman Empire, and lived on until the 15th Century AD when it was taken over by the Ottoman Turks
Islamic: ~600-1500AD: Time of the Islamic great empires, generally ends about 1500 although the Ottoman Empire extended until the 20th Century