For instance, a flat bottom tends to follow the water surface and will roll with every wave that passes. Couple this with very poor final stability and you have a boat that may flip over in rough water. Finally, a flat bottom doesn't present much lateral resistance and, thus, can skid sideways in a stiff wind. A canoe with a rounded arch bottom should have better handling characteristics. In other words, it will have great final stability.
Many canoes develop rocker when leaned because the bow and stern pop out of the water.
This makes them more maneuverable, a key element in freestyle canoeing. The rounded arch hull also sits deeper in the water when not leaned, giving it good lateral resistance and acting like a keel to help maintain course. I won't say much about materials. This is an involved subject and is better left to longer references. Suffice it to say that, for quietwater, I believe you should generally buy the lightest canoe you can afford.