I would love to add something about arrows and the differences between arrow shafts. Unfortunately, it's beyond what I know, so I need to rely on you guys to help me out. Surely there's an experienced arrow builder that would love to weigh in on this.
Don't use wood, period. It's too prone to breaking. Likewise, aluminum is a waste of time.
There are not many FG options. The Academy stuff I recall seeing is prone to splitting and it is NOT long enough. You need 28" + 2" to build the head onto in most cases. There are some specialty FG shafts but you won't find them at Academy or WalMart or anything. FG Kite spar will typically not work as shaft material because it's of a filament-wound construction and is too flexible in a reasonable diameter. Solid fiberglass stuff- driveway markers or whatever- don't use it. It's far too heavy, makes for a slow shot and typically hits pretty darn hard.
Carbon (aka carbon fiber, aka graphite) has a LOT of different properties depending on what you get. For one, there's pultruded (linear fibers only) vs filament-wound or wrapped shafts. It's hard to give generalizations because of differences in diameter and wall thickness so this is an apples-and-oranges game we cite specific models. Like there's the discontinued Blue Jacket pultruded type that was thick-walled, fairly large diameter carbon and was nigh indestructible but weighs a LOT. The WalMart stuff is typically wrapped and will generally not crack or splinter but will break in two. I use some ultra-thin pultruded stuff which gets its "toughness" from the fact that it's flexible and can be bent into a tighter radius before snapping, and it's as much as half the weight of the heaviest options.
There are also hybrid, layered shafts with a pultruded core and an outer wrap of filament-wound.
In general, this is true though: larger diameters increase the shaft stiffness. Thicker walls have a lesser effect on the stiffness but do make them tougher, yet of course increase the weight. A pultruded wall of a certain diameter and thickness will be much stiffer than wound or wrapped.
I don't agree with taping. It makes it very difficult to detect a cracked shaft which creates its own safety problem. Plus it's a significant weight and maintenance issue.