With the choice of the rudder you can influence the characteristics of the kayak to a certain extent. It is mostly the turning radius, course stability or responsiveness (e.g. for wash riding) that you want to improve.
Many parameters can work together for one characteristic but give varying results for other characteristics. For example, both length and surface area affect course stability, but resistance is mostly affected by length and only to a small extent by surface area.
In theory, a larger rudder (length & area) improves even the stability of the kayak, but the effect is so minimal that it is ignored in this review.
Length
more length provides more course stability
less length means less resistance
less length gives a smaller risk of grounding
Surface
more surface area provides more price stability
more surface area gives more responsiveness
less surface area gives (slightly) less resistance
Shape
straighter shape gives more responsiveness
backward sloping shape is better against seagrass
backward sloping shape protects better in case of grounding and again hits from paddles (eg turns at 5000 m races)
Width
a thinner rudder gives less resistance
Other factors
Heavy paddlers need a larger rudder
the further forward the rudder axis, the more force is needed for steering