I am not a fan of histories that skim millennia and condense it into one book. I find it leaves you with a simplistic and often incorrect understanding. I rather read a book on an event, say a specific war or a biography or a century. Over time, as you read more, they start slotting into place, like a jigsaw puzzle. It is more labour intensive, but if you enjoy history, well worth it, as it brings far more depth to the narrative. You can supplement this with the 'big picture'-type of books on specific topics, but I don't think it a good way to understand history at all.
In addition, it depends how you see history. Is it 'one damn thing after another', predictable processes, 'Great Men', etc. or are you looking for revisionism of Western Exceptionalism like Diamond's Guns, Germs and Steel? If the latter, try Felipe Fernandez-Armesto's books or Eric Hobshawn (if you can stomach a bit of socialist panegyric). If not, then try Niall Ferguson.
For Ancient history, few do it justice in this format in my opinion, except maybe Adrian Goldsworthy. These are all secular histories though.
I highly recommend Chesterton's Everlasting Man as well, but this is not a conventional history.