Don't know why we're stuck on hit points, but, while we're at it, here's my system.
d12-->roll d12, d10, d8, take highest, minimum of 6
d10-->roll d10, d8, d6, take highest, minimum of 5
d8-->roll d8, d6, take highest, minimum of 4
d6-->roll d6, d4, take highest, minimum of 3
d4-->roll d4, d3...