There are three near-parallel highways running North > South in the central part of Jordan. The most-traveled skirts the shore of the Dead Sea, while the Desert Highway runs to the East. Either would take you from Amman to Aqaba (on the Red Sea), in about four hours of easy driving. Between these two highways lies the old “King’s Highway,” an ancient roadway that winds through mountain towns and around tiny villages.
If you have the time, this is the road to take.
We were starting our day in Madaba, not in Amman (and I recommend you do the same, or at least start at the Dead Sea), and would be ending in the Dana Biosphere Reserve. The more direct route along the Dead Sea would have taken about three hours of driving, our more circuitous route took all day, but was full of scenic vistas and ruins.