If you have an interest in all of the works: Historical, Philosophical, Fictional, and everything in between, and want to delve straight in (which I would highly advise), I would recommend watching HBO's Rome for the reasons listed below, reading The Classical World by Robin Lane Fox, which serves as an excellent introduction to the Greek & Roman worlds, and then read The Greek Myths by Robert Graves, which gives an account of all of the main myths of Greek Mythology, which are frequently referenced in poetry and works of fiction. After this, begin with History, reading in a chronological order, then any works of fiction and philosophy you have an interest in. By reading History first you will have a better understanding for the context and time periods in which various works of philosophy and fiction were produced by their respective authors.

I would also like to echo some very good advice I was given: saturate yourself as much as you can with information about the period, people, and works, before you begin reading the primary works. This will help you get a feeling for major time periods, events, and individuals. To this end, I have listed below some podcasts and books, which you can supplement with documentaries, or anything else, at your leisure.

If, however, you have no desire to read everything, and are just looking for a way to dip your toes into the vast fountain of Greek & Roman literature, scroll down to the bottom where I recommend a short list of works which I enjoyed reading the most. You can then supplement the list with anything else that you find you are interested in. Listening to some of the podcasts below is also a great way to explore some topics which may interest you most.

HBO's Rome

This singlehandedly kindled my passion for Ancient History.

What makes the show great is that it shows life in Ancient Rome from the point-of-view of the common people, via the two main characters, as well as the emperors and patricians. It also fleshes out those names you hear so much into fully formed, living, breathing, people.

This is the real beauty of the show; it shows you that those people who lived so long ago were real people. People like us.

After watching it, you can put faces to names (like most HBO shows, the casting is perfect) and the Romans become real. Caesar, Cicero, Augustus, Cato, Scipio, Marc Antony, Cleopatra; these people live and breathe.

The set and costumes are incredible (the largest set ever built), and was cancelled due to being too expensive; it cost more, back then, than Game of Thrones did in it's infancy. In this incredibly expensive, lavish, gritty show, Rome and the ancient world come to life.

You could watch the 1976, thirteen-episode series, I Claudius (based on the novels by Robert Graves), as a sequel to Rome.

Podcasts

In Our Time

The topics below are listen in roughly chronological order.

Ancient Greece

• History of History
• Trojan War
• Greek Myths
• Homer's Odyssey
• Sparta
• Thucydides
• Thermopylae
• Battle of Salamis
• Tragedy
• Aeschylus' Oresteia
• Library of Alexandria
• Socrates
• Plato's Republic
• Plato's Symposium
• Aristotle's Politics
• Aristotle's Poetics
• Greek & Roman Love Poetry
• Alexander the Great

Ancient Rome

• Romulus & Remus
• The Roman Republic
• Hannibal
• Julius Caesar
• Cleopatra
• The Augustan Age
• Tacitus and The Decadence of Rome
• Agrippina The Younger
• Aeneid
• Ovid's Metamorphoses
• Roman Satire
• Pliny's Natural History
• Pliny The Younger
• Stoicism
• Seneca The Younger
• Rome and European Civilisation

Emperors of Rome Podcast

This is a great podcast with Matt Smith & Dr. Rhiannon Evans, and, later, with Dr Caillan Davenport, and discusses not only the Roman Emperors, but various other figures, and social and political topics throughout the Roman Empire.

The History of Rome Podcast

An epic undertaking by Matt Duncan, this podcast goes through the History of Rome in no less than 179 episodes. I wouldn't recommend listening to all of these before reading the primary works (perhaps during or after?) but it's an excellent source of information.

Books

• The Classical World - Robin Lane Fox

An excellent introduction to Greek & Roman History, this grand narrative begins with Homer in the 8th Century BC, and ends with Hadrian in the 2nd Century AD. It is very accessible, and contains an excellent, detailed, well-organised, bibliography of some 30 pages.

• The Greek Myths - Robert Graves

A very detailed account of all the main Greek Myths from early creation myths to the journeys of Odysseus.

• Classics: A Very Short Introduction - Mary Beard, John Henderson

This looks like a great introduction.

• Confronting the Classics - Mary Beard

Goes into more detail than the VSI above.

• SPQR - Mary Beard

Like the previous two, I have not read this; but I enjoyed Beard's Pompeii, and this well received work looks like an excellent history of Rome beginning with the foundation, and ending in the 3rd Century AD.

Reading the Primary Works

Personally, I started with works of History, then Fiction, then Philosophy, reading all of these in a chronological order. Reading chronologically has enormous advantages; it provides you with a clear perspective and narrative throughout time, and you can also pick up on any references made to previous historical events, authors and their works, and philosophical ideas.

I had an interest in all three types of works, and decided that reading them chronologically was the best course to take.

However, if you do not have a desire to read everything, and simply want to explore some works of classical antiquity, I recommend below some works which I enjoyed reading the most.

History

• Herodotus' Histories

The first work of History, Herodotus' work and paints a fascinating portrait of the ancient world.

• Xenophon's Anabasis

Xenophon's tale of the March of the Ten Thousand is incredibly entertaining.

• Arrian's Anabasis

Arrian's entertaining account of the campaigns of Alexander the Great.

Fiction

• Homer's Odyssey

An epic adventure. 

• Catullus' Poems

Powerful and passionate poetry.

• Ovid's: Metamorphoses, Heroides, Love Poems

The Metamorphoses provides an epic account of Greek & Roman mythology, the Heroides are short letters from various Greek & Roman figures, and his Love Poems are very entertaining.

• Horace's Odes

Horace's Odes are an amazing collection of poems on a wide variety of topics

• Martial's Epigrams

Highly entertaining, Martial pours wit, sarcasm, and humour into his Epigrams, and in so doing, brings Rome to life.

Philosophy

• Plato's: Euthyphro, Apology, Crito, Phaedo, Alcibiades

The first four works are collectively called The Last Days of Socrates, as they give an account of the final days of the great philosopher, and his trial and execution. Alcibiades is now commonly thought not to have been written by Plato, but it was thought as an excellent introduction to Plato's philosophy in antiquity, due to it's emphasis on self-knowledge.

• Aristotle's: Nicomachean Ethics

Aristotle's highly influential treatise on Ethics.

• Seneca's Complete Letters

One of my favourite works, and only a few pages each.