I use the natural taper of the shoot and reduce the butt end if necessary. Your best bet would be to collect different sizes and experiment to find what works best for you. Hillbilly and I both use sourwood but we work them differently. Steve(Hillbilly) likes to make his shafts look like machined dowels(all with hand tools) and I like mine to be as crude as possible but still effective. Art Butner, who got me started with sourwood and taught me lots about making arrows makes sourwood(or any other material) arrows that will rival any arrow from any material by any arrowsmith. Art's arrows are truly arrow Art! So, take all that you can read about making hardwood shoot or cane arrows and experiment to see what works best for you. There is no right or wrong way if they make arrows.
Privet is excellent arrow material. It is hard and heavy!