There is not one single Ancient Greek but different dialects from different times and places. The ones that are commonly studied are Homeric Greek, Attic Greek and Koine Greek.
Epic Greek is more or less the same as Homeric Greek. If you want to read Homer, this is obviously what you should learn
. It's the oldest dialect of the three.
If someone says just "Ancient Greek", usually that means Attic Greek. It was spoken in Ancient Athens and it was the language of Socrates, Plato, Aristoteles, Aristophanes etc.
Koine Greek is about the same as New Testament Greek. It was spoken in large area around the Mediterranean after the conquests of Alexander the Great, a bit like English is now spoken widely around the world.
The ancient dialects are not very different from each other, so if you know one it's easy to learn another. Modern Greek is quite different, like Latin compared to Modern Italian.