Canoe Sounds Good…
...for your intended uses. We canoed and camped with our daughters when they were young, and they loved being on the water and in the woods.
As to the best design, that's hard to say; kinda like do you prefer Chevs or Fords - all depends on what you want to do, and your preferences. I'd be inclined to look for something with reasonable beam and a fairly flat bottom (good initial stability) without huge areas of topsides (windage can cause problems in stiff breezes)in the 16' range - that'll be big enough to carry weight as your son grows and you perhaps want to do some canoe-camping.
Re kayaks - I'm not a big fan of kayaks for paddling with children. Most tandem kayaks are pretty large for a single paddler to handle, and putting a child in a spray deck in that forward cockpit makes me really, really nervous. Now that our girls are long since on their own, Chris and I do have sea kayaks and seldom use our canoes anymore, but for family paddling I'll take a canoe hands down anytime.
For a first canoe, I'd strongly suggest looking around for a used boat - you can get great deals (like 1/2 retail), and have a chance to talk with someone who's paddled the craft and knows its strengths and weaknesses. If it doesn't suit or you outgrow that boat, you can resell it for something very close to your investment instead of taking the loss on a new boat.
You should also test-paddle any canoe before buying - if it feels comfortable on the water, it'll be OK as your first boat. Take your time selecting a canoe, and learning to use it; there's a lifetime of enjoyment waiting for you and your family.