A good website to find out what to bring on a cruise ship is, Packinglistplace.com. Look under the cruise ship listing. That should give you most of the information that you seek. Make sure you print out a list for both of you, that way, you won't get confused about what you are packing. It also gives you extra space to write in something that you might not see on the list that you need to carry with you.
You definitely want to carry all your essentials with you on your carry on bag, because it will be several hours before you see your other luggage that will be delivered to your cabin. You will probably need to bring a formal outfit for 1 formal night, if you want to. To cut down on the packing, try to have garments that you can mix and match for different look