The key here is to plan the meals. If you know all the dinners you will make you will know what pots etc you need. That said:
- Plates 1 per person + 2 or 3 for cooking purposes
- Mugs 1 per person, more if oatmeal is a morning thing for you
- knives, forks, spoons 1 per person
- wooden spoon, tongs, flipper, ladle (or mug as ladle) according to the meals you plan
- 1 large pot for rice or pasta for the group, and its lid
- 1 smaller pot for sauce to go on that rice or pasta
- 1 stove [*] (Cook sauce first and set aside then cook starch, or cook one pot stews etc) and enough fuel to run it for the total time all your meals, morning coffee, dishwater, and washing water will need
- a camping kettle
- a non stick skillet for pizza, first night steaks, morning bacon, English muffins etc
- sharp knife and thin cutting board
- something you can measure "1 cup" or "300 ml" of wet or dry ingredients with
- washing up bowl(s) - see https://outdoors.stackexchange.com/a/5980/163
- Nalgene bottle for soaking dried meat in all day or beans overnight - reserved for this, don't use someone's drinking bottle
Work through your meals to see if you need a grater, strainer, can opener etc. You can usually get by with less but one of the luxuries of canoe camping is being able to have cooking equipment.
And of course you'll need your ingredients, spices, salt and pepper and the like.
[*] I would NOT recommend a two burner Coleman-type stove. I've done it, but it's just too heavy and too hard to carry in a backpack. We save that stove for car camping these days. I've used a wide variety of stoves over the years and am now happy with my WhisperLite, though it is famous for not simmering well. If you choose to take two stoves - and when a group gets above 10 you may need to use two pots to cook enough volume for that many - I would recommend two different stoves (so their strengths and weaknesses balance) that use the same fuel. But the details of what stove to get probably belong in another question anyway.