We are on the morning tour at Highclere Castle on Sept 4, 2018. What timed ticket should we buy for Stonehenge?
It’s close to an hour drive, it depends how long you are at Highclere Castle.
If we get to Stonehenge by 4pm, is that sufficient to have a good visit there?
Yes, 4 PM is sufficient to be allowed entry, but if you can manage to get there a little earlier it will be better. English Heritage says the last entry is 2 hours before the announced closing time, which in September is 19.00 (7 PM).
See http://www.english-heritage.org.uk/visit/places/stonehenge/prices-and-opening-times
To drive from Highclere Castle, take the A34 south to the major roundabout at the A30 / A303. The sign on the roundabout will say Andover. After that, follow signs toward Exeter. There is often a queue (traffic backup) before the junction for Stonehenge, so be prepared to brake.
I believe it is possible to visit Woodhenge and Durrington Walls after Stonehenge closes; located just north of the A303 on the A345.