Normal
For Barcelona, I'd recommend arranging your own air. As you will be flying from New York, you should be able to get a non-stop flight. Cruise line air arrangements can put you on any combination of flights. On our trip to Barcelona (from Boston, via Madrid), our luggage was not put on the plane in Madrid until later in the day. My BIL and SIL had the same experience on the reverse trip. So, I'd advise going non-stop whenever possible, if the cost difference is not huge. (For Europe cruises, they are sometimes around the same.)Edited to add: I totally missed that your return is from Venice. I'd suggest calling your TA or NCL to inquire about the price for these flights as they are called open-jaw (arriving to and returning from different cities), and they may be less expensive through the cruise line. Then, check the pricing yourself on Orbitz or a similar site (without purchasing) to determine what is more worth it to you.
For Barcelona, I'd recommend arranging your own air. As you will be flying from New York, you should be able to get a non-stop flight. Cruise line air arrangements can put you on any combination of flights. On our trip to Barcelona (from Boston, via Madrid), our luggage was not put on the plane in Madrid until later in the day. My BIL and SIL had the same experience on the reverse trip. So, I'd advise going non-stop whenever possible, if the cost difference is not huge. (For Europe cruises, they are sometimes around the same.)
Edited to add: I totally missed that your return is from Venice. I'd suggest calling your TA or NCL to inquire about the price for these flights as they are called open-jaw (arriving to and returning from different cities), and they may be less expensive through the cruise line. Then, check the pricing yourself on Orbitz or a similar site (without purchasing) to determine what is more worth it to you.
