Just to name a few things to think about when choosing fletchings.
FOC, the lighter the fletchings, the more FOC you will get. Feathers are about the lightest.
Speed, the more drag you have on the back of the arrow, the less speed you will get and the lesser the trajectory will be (usually beyond normal hunting ranges).
Stabilization properties. The more the arrow spins and the greater the surface area in the fletch, the greater stabler the arrow will be. A fixed blade broadhead will be better served by a stable arrow.
Quietness, I believe that tests have shown that a parabolic cut is the quietest, followed by shield andbanana.
Peronally, I love the Pope and Young cut feathers. However they are a bit loud. For hunting, I use a banana cut. Both are pictured below.
If you are shooting off the shelf of a bow, you must use a feather.
Per