Traditionally the starting point is Istanbul, because most of the overlanders came and come from Europe and travel overland via Greece to Turkey. Another plus of Istanbul is that is has cheap flights from most of Europe.
If you are from outside of Europe (Oz or North America) and want to go to Syria or Jordan the cheapest way is usually via Europe and Turkey for Syria and via Europe and Egypt for Jordan. This is because flights to Damascus and to Amman are usually for business, not for pleasure, few airlines serve them and thus the higher prices. Turkey and Egypt however get plenty of package tourists, thus lots of competition and sales for empty seats on charter flights. So travellers on a budget headed for Syria or Jordan fly into Turkey or Egypt and take the bus (or the ferry from Nuweiba to Aqaba) over the border.
If you are on an RTW ticket you'll only get a decent price for a ticket that includes Damascus or Amman if you are coming from Asia and fly with an alliance that has Emirates or another gulf airline as a member. Covererage of the Middle East on RTW flight networks is not very good.
If you need to choose between flying into Amman or Damascus I strongly recommend that you fly into Damascus. Amman is one of the most ugly cities in the Middle East. It is a city to pass through on your way to Israel or Egypt when coming from Syria, but not much more.
[ Edit: Edited on 30-Jan-2009, at 15:54 by t_maia ]