I have made a few arrows with goldenrod, horse weed and dog finnel; all perennial weeds. Chris' advice about collecting at the appropriate time is good. It doesn't take these weeds long to start deterriorating. I have a horse weed arrow that was sent to me from Jamie after killing a doe with it out of my Medicine Bow. The point was gone but the shaft is still sound.
For shoot arrows; rose, sourwood, viburnum, etc, you want to collect at least 2 year old shoots. The easiest way to determine if they are at least 2 is there will be small branches where last years leaves were. When the leaf falls off it leaves a leaf scar. Usually, at the top of this scar will be a bud that will make the small branch next year. First year growth is usually pretty flimsy and not good for arrows. By the second year, you have 2 growth rings that will work against each other to give you a stiffer shaft. You can adjust this stiffness, if it is too much, by sanding or using a thunb plane to remove some wood from the center of the shoot to reduce the spine. Pat