Hello, fairly regular cruiser here, although also not with MSC. I usually take a mix of lightweight dresses/shorts/t-shirts for the daytime. Pair of comfy flat sandals/skater/Converse-type shoes for during the day onboard ship and also sightseeing.
The cruise line that we go with (P&O) still have formal nights, so I have evening dresses and DH takes a dinner suit. Otherwise, the dress code is 'Evening Casual' so I pack what I would wear to a nice restaurant over here (trousers which nice top or a dress). I try and take just a couple of pairs of heels/sandals for the evening, usually one in a neutral shade and one in black which will go with all evening outfits.
Some ships can get quite cool in the evening (air conditioning is sometimes a bit fierce) and also if you go out on deck it can be breezy, so rather than pack a separate jacket I take a couple of pashminas, again in neutral shades that will go with everything.
DH takes similar to me for the daytime - jeans/light trousers, shorts, t-shirts/polo shirts. For the evening he's got smart trousers and a number of smart short sleeved shirts. Sometimes he'll take a jacket as well, and he will take his dinner suit for formal night.
I agree that forums like Cruise Critic are invaluable sources of information if you are not sure of anything or post on here - one of us will pop up to help!
Hope this helps, and have a great time!