Dianne H,
I'll give your questions a try: On-line travel agent? If you're a frist time cruiser on-line travel agents aren't generally recommended because you have questions, like about the airline tickets. If you feel confident you've understood about travel insurance, the different cabins, dining choices, etc., you can give it a try (costly, but survivable--maybe a cabin poortly positioned, maybe not your preferable seating, etc.).
Airline tickets at time of cruise purchase? I think this kind of flight is called open-jaw, where you're coming in at one airport and leaving from another. Usually these are quite costly on your own. Princess will probably have a charter flight into Venice. So if you can't do it cheaper and timely, you buy the flight with the cruise purchase.
That said, if you could make it into Venice on April 10 (you'd be sure to make the cruise because it stays overnight in Venice anyway) and take a train from Rome to Venice at the end of the cruise, that may be a less expensive alternative.
The intensive itinerary? Get a go-go attitude if you want to do it all. Watch the times and length of the tours you're booking. I remember the Athens tours have a side trip to the Temple of Poseidon, that's a 1 1/2 hour coach ride one way in addition to the tour of the city. Look at the day before and the day after schedule. (Coincidentally, in this particular example, the Captain will probably announce when he is passing the Temple because they traditionally throw a tribute--I think a glass of wine.)
The tour I think is the most desirable for a first time visitor is the trip along the Amalfi coast when we go to Naples.
So much for my try. If you have other questions, just ask.