I have used 10' and 12' NuCanoes for slow-river paddling, including upriver paddles, cruising thru rocks, river cleanups in faster water, etc. They handle Class I rapids like a raft. They are very maneuverable, ridiculously stable and quite unsinkable. I had a 12' out on a whitewater section of the French Broad and while it got stuck a lot (and got completely full of water once), it did not flip or go under.
They're wider than any other kayak, so get the NuCanoe paddles.
Touring Kayak Paddles
2-3 Canoe/Kayak Trailer