A big part of this is "which canoe? which kayak"
A long paddle in a white water kayak is a pain. They are slow. Ocean kayaks are much faster but are less than nimble to turn.
I find the position in a kayak uncomfortable, and painful after about an hour or so.
Canoes also come in whitewater versions, with a fair amount of rocker, and full bow and stern, and flat water versions that slide like grease over a calm lake. And countless compromises in between.
Another part of the equation, "How long?" How long are you going out for? White water kayaks can be used for a weekend trip, but access to your gear is awkward. A 14-15 foot solo canoe can easily carry supplies for a month.
I'd go with a canoe, with a somewhat vee bottom (better secondary stability) fairly straight keel line (If I want to turn it, I'll lean it.) somewhat flared ends. For long trips, 15 feet, for short ones 14 feet. (That extra foot is in the middle -- makes a big difference to cargo capacity)
In your case, since you aren't into white water, a straighter design may be more appropriate.
Many places that sell canoes will also rent them. Many canoe clubs have a fleet of loaners. And you can swap time on weekend trips. Paddle a bunch of canoes, and keep notes as to their characteristics.