As you can see by Steves links, there really is no option from Trieste. Most ferries leaving from there head into Croatia, so Venice is the better choice. You may also notice that it is a long trip, 29 to 35 hours, then once at Patras, several more hours to Athens (If that is your destination). While I do not want to interfere with your plans, in my opinion ferries are more like buses(with less to see) than cruise ships. You may want to consider flying to Athens, Aegean Air operates out of Venice and will get you to Athens in a morning, sipping Ouzo in the Plaka while the Ferry is still a day away. Even if Athens is not your destination, travel connections are probably easier to anyplace from Athen than from Patras.
As for Cappadocia, you do not mention the length of the trip, but it is a long complicated trip to there from Greece. Flying would be highly recommended due to the distance, but you would need to get to Turkey first in order to catch a low priced fare. If you will be in the Greek Islands, you can get to Samos, take the ferry to Kusadasi (see Ephesus) then catch a budget flight from Izmir to the Cappadocia region, to get to Cairo will likely mean Flying to Istanbul and then a Flight to Cairo.