I think it's time to go back to Rome

Adrian Goldsworthy, no slouch when it comes to the classical world, has this to say about The Classical World by Robin Lane Fox.

Lane Fox's survey deserves to be widely read. Indeed, I cannot think of a better introduction to the subject for those with no prior knowledge. ...Lane Fox's strong and clear narrative will stimulate those reacquainting themselves with this fascinating era as much as it enthralls newcomers.

From the description it appears to avoid the trap of squeezing all of history into a brief narrative, instead focusing on key themes.