If you like a high end AI, you’ll be all good with a mid range cruise line!
Pay the extra for a room with a balcony. P&O are very “middle of the road” but have a very good range of destinations in Europe.
I would say Marella, MSC and definitely Costa are below their standard.
Princess, Celebrity, Royal Caribbean slightly above.
Then you have your Cunard and your super high end stuff like Azamara, Seabourn etc. None of which I’d take a 6 year old on.
My personal favourite is Royal Caribbean. For the money, what you get on the ship is incredible and we find on the bigger ships, there’s much more variety of things to do in the evening. For example, Anthem of the Seas is my favourite ever ships- the pool are is split between an adult only solarium style, a normal outdoor pool and a kids splash area. It had a whole indoor gaming area with table tennis, laser tag, go karts etc- this was great in the evenings as usually very quite.
Evenings there was a theatre with your usual selection of musicals (including a full length production of We Will Rock You!), singers, circus acts etc. At the other end of the ship was a super high tech lounge that doubled up a place for quizzes/game show style entertainment but also had a phenomenal laser driven cabaret. In the middle of the ship was a pub that did pub quiz/kareoke/live solo singer type entertainment. Our favourite was the piano bar with just a single pianist taking requests night after night. There was also a night club and evening kids stuff.
Basically it was take your pic with things of varying different vibes in different areas of the ship, which really spread out the different “crowds”- the drinking crowd were usually in one area, the quiet adults in another, families elsewhere. They really catered to all tastes. Similar concept again with the restaurants. Everything from a casual grab and go pizza place, to a huuuge buffet, formal dining room etc!
It also sounds like the ports are important to you- pick one that has a high ratio of port days to sea days and you definitely won’t get bored.
One of my most interesting itineraries was a mix of Turkish and Greek ports, with only one day at sea.
It sounds like you want hot, but a good “first timers” cruise with lots of interesting things to see and do is Norway. It’s generally Day 1- Board in Southampton, Day 2, Sea Day, Days 3-6 in port and then one more sea day back in Southampton. As you’re in the fjords, the scenery is always amazing and the ports really vary- Stavanger is a popular town, Bergen is a full city but you usually also get a few that are a village deep into the fjords with amazing scenery and the chance to see glaciers/snow capped mountains.
I’d avoid Citivechhia (may have spelt that wrong!) for Rome, Venice (they hate cruise ships!) and anything that says Paris or Amsterdam as they are known for being absolutely miles away!