The high season for Mediterranean cruises begins right now, from the end of April to the middle of October, and if you have booked you will want to know what you put in the suitcase, from documentation to clothing or other things, such as a plug adapter. What I would tell you is to ask at the agency, or read in the different blog, how are the customs of the countries you are going to visit.
If I focus on clothes, like any cruise I will tell you to wear comfortable clothes, You are on vacation and you will surely take advantage of it to do a lot of excursions, so the footwear must also be appropriate.
And don't forget it you are in the Mediterranean, so swimwear, if you wear a bikini you will have to wear both pieces for bathing, for sunbathing, in most boats it is not necessary, or specifically indicated in the pool, cap, sunglasses and sunscreen. In my case, I always prefer it to go above factor 30.
A recommendation that I usually make to the inexperienced is that they wear a small or medium backpack in which to carry everything you need to start the cruiseSo while you board the boat, you can already enjoy the ship's facilities… it is the best time to try the pool.
I remember you, If you are going to do excursions that include religious places, such as monasteries and churches, which usually ask for “decent clothes”, Tops, strapless necklines or shorts or skirts that are too short are not understood in this sense, so it is always recommended that you wear clothes that cover your thighs, arms and shoulders. You can wear a scarf that helps you cover yourself, so you can access these churches and monasteries without jeopardizing your entrance.
And as a last recommendation I would tell you that put on a thin raincoat, there may be some other summer storm, especially in the late afternoon.
I recommend that you also take a look at this article about the essentials that you should carry in your suitcase if you go on a cruise. Happy crossing.