Is 600 bce a good date to end early time period of world history

Yes, that, I think is perfect.  When I think of early world history, I think about Babylonian times (before that would be Pre-History) to the founding of Rome. Then from the founding of Rome to the fall of Rome would be what I call the Mid-History.  After that would be Medival times all the way to the Renaissance and from then on, I consider it as modern history.  Of course, this will probably change in the future.  Plus, this is only the periods of history in Europe, Africa and the Middle East.