I have a fair bit of experience in kayaks and none in canoes.
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My impression of canoes is that of it being more akin to small yachts where you sit on a bench from where you row or paddle, although I have seen competitive canoes where you kneel and are strapped in. My guess is that when canoeing it might be possible (I don't know) to keep your hands dry.
I know someone who was a really good kayaker but got injured and could not use a two bladed paddle. He got a whitewater canoe (1 man with a good rocker). It was very good up to grade 5 rivers. It wasn't much bigger than a modern whitewater kayak at the time (not a freestyle type more the creeker type). He turned out to be very good in a canoe too. So he replaced it with a freestyle canoe. Best way to describe that boat was unstable. One by one all the kayaker in our group tried it out on a very easy stretch of a grade 3 river (not really grade 2 at that spot). Not one could get it that far out of the eddyline without getting thrown out.
Anyway, this guy, who was really talented, could play on grade 4+ rapids and do tricks on grade 3 playspots. It had airbags to stop water filling it. Difficult boat but very impressive performance in the hands of a good paddler.
If you like a challenge and like whitewater kayaking seriously try your hand at a proper whitewater canoe or even a freestyle one. You might be surprised.
But back to the OPs question. Join your local club. Best advice you can get. It's not just the social aspects but you learn from some very experienced local paddlers. Local knowledge is useful to say the least.
Boats? Flat water inland touring kayak. Long, decent speed, storage and good in wind. Sea bays, estuary and inshore water then a sea kayak. Like a flat water touring kayak but better for sea. Double hatches and sealed storage that they access. These two can also have skegs, basically a fin in the tail that can be raised or lowered to help with straight line tracking.
Canoes are great boats for their uses. Load carriers, good for two or even three, good boats for centre use on lakes. In the hands of the experienced they are on on whitewater to up to a certain level.
Lakes. Well bear in mind that if you lose control on the middle and capsize you'll have a long way to go. You might be ok but your kid? Stick to paddling close to shore until experienced unless you are with a group that can help you out. A club is good for that. Also note lakes can get choppy too. I've seen waves that have been wind whipped up and that made it very hard to paddle in a straight line on the direction I wanted to go. Very tiring at times. The sea is a lot worse.
Not trying to put the OP off but kayaking is something that you need to learn about. Courses and groups are my advice. I took a long apprenticeship in my paddling but one day I found out I was a good kayaker. It was when a very senior examiner I often paddled with in a close knit group told me I handled my boat well. I think that took 10 years or more. I still can't work out when I stopped being a novice though.
Of course when you'd learn your paddling in whatever type you choose then you'll have skills to enjoy an amazing hobby. You can see and experience things by small boat like kayak or canoes that you can't by any other means. For example, off holyhead Island on Anglesey there's a coastline made up of heavily folded rock layers. Every so often there's tunnels or cracks that a kayak can get into. One such tunnel leads to a hidden bay with cliffs all around the beach. I do mean around including the sea side where the tunnel comes from. Actually tunnel is wrong word, it's a cave or crack.
Our river paddling where you're going down rapids watching a dipper hunt in the water. A dipper working their own stretch of river never gong into the territory of the next one. Beautiful bird IMHO and very interesting to watch.
All theae things and more you could experience but do it safely with others.