Ay-yi-yi! This is a very broad question, a true answer to which would probably require a PhD in hydrodynamics or years of relevant engineering expertise. Note that the interplay between these design characteristics can be very complex and depend greatly on the exact conditions (flat water / waves / moving water / rapids / ..., skill of paddler, travel speed, ...). Furthermore, there are many, many, many other design characteristics that could be considered (freeboard / keel / bow shape / hydro-planing / ergonomics / ...), as well as considering that the hull shape varies over the length of the boat.
All that being said, here's a very rough guideline.
Much can be learned by comparing images of modern boats and considering the intended design. In comparing the general hull shapes, let's try to reverse engineer the design.
- A crewing scull is built to travel as fast as possible in a straight line over absolutely flat water. Stability is of minimal concern; all that matters is speed. Consider what can happen at even the Olympic level with a little bit of chop (or purportedly a blade snagging a piece of floating garbage). While there can be some very complex hull designs, a scull will generally have: a long narrow plan, a chined cross section, and very little rocker.
- Sea kayaks are generally built for covering long distances on reasonably flat water, generally with few course corrections. The paddler has some ability to provide active stabilization in a well fitting cockpit. A sea kayak generally has: a long narrow plan, a chined cross section, and a slight rocker.
- Canoes are also generally built for covering long distances on reasonably flat water, generally with few course corrections (note that there are whitewater canoes, which look very different).Passengers are located higher off the water in a canoe than in a sea kayak. Thus, a canoe has a higher center of gravity and lateral stability is more of a concern---passengers have less ability to provide active stabilization by shifting their weight. A canoe generally has: a long narrow plan (although wider than a sea kayak), a flat cross section, and some rocker.
- Whitewater kayaks. Whitewater kayaking requires frequent changes in direction, with much of the stability coming from the paddler actively balancing and maneuvering. Most of the forward movement comes from the current---actively paddling downstream is generally inefficient. Many designs are also built around surfing waves / playboating / whitewater rodeo. A whitewater kayak generally has: a short wide plan (often limited by leg length), either a flat bottom with hard chines or a gradually rounded bottom, and a lot of rocker.
Now that we have a handful of actual boat shapes, let's look at each of this hull characteristics in turn. Assume that we are tweaking each of these parameters in isolation (i.e., all else being equal), along with many other disclaimers.
A longer, narrower plan will generally result in less hydrodynamic drag (particularly dependent on the bow shape). It will also generally track straighter, but at the cost of reduced lateral stability and more difficulty turning. In comparison, a short wide plan would easier to turn and more stable, but give more drag and be slower.
A flat bottom will provide the most lateral stability (and usable interior space), but will have a harder time tracking straight. It will also "skid" or "pivot" turns, unless actively tilted on edge.
A rounded bottom will be easier to tip from side to side, which can be beneficial in a kayak. It will behave somewhere in between a flat bottom and a hard chine, depending on how rounded it is.
The "vee or hard chine" cross section will generally track straight, as it has somewhat of a keel effect. This shape also has a secondary balance point when the boat is tipped on its side, allowing it to "carve" turns (this is how you turn a sea kayak, for example). On the flip side, this shape is difficult to turn in place.
For rocker, we need to consider how much of the boat is in contact with the water (freeboard vs. beam, etc.). A more pronounced rocker will
- Be easier to turn (starts to emulate a short, wide plan if we look only at the portion of the hull in contact with the water).
- Be able to ride up and over waves as opposed to punching through them.
- Be more prone to "planing"--rising up out of the water with increased speed. Think of a speedboat rising up out of the water as it hits high speeds.
- Be somewhat less fore/aft stable.