Hello there Will! Thanks very much!
As for fletching, there is a lot of differing opinions and speculation about fletching types, also about stability vs. distance between heavy, light, bob-tailed, barralled arrows etc.
Ideally I prefer a rounded triangular shape as I find it ideal in straight flight and superb distance while the trailing edge of a traditional medieval arrow looks nice I think, but it is a bit more cumbersome between the fingers, restricting ( a miniscule amount) how far back on the shaft the feather can be seated. A small matter true, but if we are speaking practically for the best performance of an arrow all these tiny factors begin to become ever more relevant. Therefor I would choose the rounded triangular shape if my life depended on it and if I had the choice!
However, the varying feathers are due to Society arrow spec regulations. For example; an EWBS 1/4lber requires a trailing edge as nature intended, where as the EWBS livery must be triangular. An EWBS-NZ Sheaf arrow also requires a trailing edge as nature intended where as the EWBS-NZ bearing allows a rounded slope etc.
The reasoning for the strict arrow specs is to, for one, give an equal playing field for every archer internationally allowing them to see and compare their progress with everyone else with as much emphasis on the archer's skill instead of his equipment as possible.
But even more so they come from what physical evidence we have left from the period. Detailed analysis of arrows has been done by many individuals, which makes up for much of the information available to us today, the rest can be obtained from manuscript images.
Take a look at a few of these I have on my desktop here:
Now keep in mind these are just the few I have at the minute but take a good look at the fletchings and the shafts and the heads. Many will be glorified and a significant amount of artistic license must be acknowledged, but the first image in particular I quite love of a fletcher's workshop holding what looks like an exact replica of our modern livery arrow only with a bulbous nock commonly used before inserts.
Now this I think more than anything is what I would recommend basing your arrows off of. But I could go on for a whole threads worth on such things. In the end, be as true to the history as you can, and the only way to do that is through the limited knowledge we have to go by.
Hope this helps!
-Jake