Choosing a feather shape:
Feather sizes and shapes are largely a personal preference. Longer feathers will increase the drag on the arrow, causing it to not fly as far. However, longer feathers are necessary to stabilize heavier arrows and heavy tips.
Right wing vs. left wing
Flu-Flu's were designed for bird hunting and their very large feathers keep the arrow from flying too far when it is aimed in the air at a bird. They often have four feathers per arrow instead of three and other modifications to the arrows to help increase drag.
As their name implies, right or left wing feathers are the flight feathers from the right or left wing of the bird. There is no advantage to shooting with one type or the other, but you never want to mix types on an arrow or between arrows of a set. Fletching jigs are setup for either right wing or left wing, so make sure your feathers match the type of jig you are using. Flight feathers have different textures on either side of them, one side is coarse and one side is smooth so they can be used for flight. This changes the way the air flows over them, and when used in arrows, this property will cause the arrow to spin. If different types of feathers are used in the same arrow, the aerodynamics will be compromised.