Hull shape affects performance
Depending somewhat on width, flat or smooth-bottomed kayaks (U-shaped) have more secondary stability, while keeled kayaks (V-shaped) have more primary stability. U-shapes may feel tippier at first, but stay stable in moving water (rivers, surf, etc.) while V-shapes feel most stable in flat water. The tri-form hull of most sit-on-tops combines both primary and secondary stability with a long center keel to keep you going straight, and two "shoulders" that act like sponsons for secondary stability. This tri-form hull generally sacrifices a little speed, but adds a lot of stability (which is great for cross-over sports like fishing or diving).
There are lots of different hull shapes, but basically V-shapes encourage a boat to go straight (good for touring), and smooth bottoms encourage a boat to spin (good for surfing, kayak polo, or river running). Whether or not a kayak goes straight is referred to as "tracking." You'll want a kayak with good tracking to cover distance on flat water, but you'll want less in whitewater. Chances are, for recreational paddling, you'll want a kayak with a keel (some kind of V-shape on the bottom), so you can travel more efficiently. If you expect to spend equal time on flat and moving water, consider buying a short kayak with a keel (it's all a continuum, remember).
"Rocker" is another term used to describe hull shape. Think of the keel as something you'd notice on a kayak cut in half. Rocker is most noticeable on a kayak cut cross-ways. A kayak with a lot of rocker would look like a "U" in a cross-ways view. A kayak with little rocker would look like a line. Keeping in mind the idea of surface area and water displacement, you'll want a lot of rocker (one round point touching the water) for maneuverability, and you'll want very little rocker (a long, thin line of points touching the water) for touring. For recreational paddling, pick something in between.