My opinions on most common shaft materials
Purpleheart: Heavy, stiff and hard-hitting with a high pitch sound. Perfect for Break/jump applications. IMO not so good for playing, but can be used, obviously. I tried a playing shaft made of purpleheart. To me it felt kind of dead.
Hornbeam: Somewhat less stiff than purpleheart. Used in carom cues, mostly cheaper ones. Reminiscent of maple, but IMO not as good as the higher grades of maple. Has a stronger spine.
Maple: Everyone knows how maple hits, right?
Ash: A shaftwood material with some drawbacks, but can be worth it. Mostly used in snooker cues. Ash needs to be covered by an oil finish, in cheaper cues laquer can be used (but is terrible). Without the finish, it will snag your beard (painfully). Also it has prominent, black grain, which some find ugly. The black color comes from "grain filler". The natural state of the wood has grain only slightly darker than the rest of the wood.The grain is harder than the rest of the wood and wears slower, which can become a problem, but only in extremely old cues.
Ash has a softer, lower toned hit than maple and can feel more springy. The lower grades of ash cues are complete garbage (as sold by for instance Riley). They feel dead, soft and will often warp. But the higher, selected grades of ash feel wonderful and give a degree of finesse that IMO surpasses that of maple. After having played with my quality ash cue, using a maple one is always somewhat of a let-down...It's like going from a brand new Moori tip to one that is in the later stage of it's life.
Pearwood: Used in some, older English billiards cues. A wonderful, smooth and soft hitting wood with a lovely golden colour. Not sure if it's any good for pool cues. If you want a high pitched "ping", this is not the material for you, obviously.
Maple cored fiberglass: Lots of world championships have been won with these, and they actually hit acceptable, when compared with the very cheapest and worst of the maple cues. They have a muted, lower pitched hit than maple. The issues are mainly friction and durability. They need to be treated with specialized cleaning agents to remain slick, and once you get a dent, it's there to stay. Nothing you can do to get it out. Sanding is out of the question.
Graphite: Plasticky and with lots of vibrations. Never tried one I found even remotely acceptable. Cannot be sanded/repaired. Avoid.
Aluminium: Tried one, and didn't like it one bit. Very funny feel that is hard to compare to wood. If you wish to know how it would feel like to play pool with a cue made of lots of beer cans, glued together, then this is the material for you.