SportStop Stainless Steel Self-Tapping Lacrosse Head Screw
2) Long but not too long. Sometimes these brands have a 1" screw which is way too long for what you need. So ours is more than 1/2" but much less than 1".
3) Diameter must be right. If the screw it too thin, it will not work with some of the existing pre-drilled shafts and even when it does it wears out too fast.
4) Stainless steel. We did not try and save a few cents on each of these screws by getting a regular steel screw, instead we went with stainless since it is strong and will not rust.