I got my osage lumber and bamboo from 3riversarchery and my bloodwood and purpleheart from a hardwood shop. Starting dimensions were: osage at 5/8", bloodwood and purpleheart both at 3/16" each, and bamboo at 1/8". Bow is 1 1/8" wide at the fades and is parallel for half the limb, then tapers to 3/8" wide tips.
If you are only restricted to the woods you mentioned, I would say HHB, ash, and cherry are your best bet, for a trilam. If you are willing to spend a little on quality, i cand recommend osage enough for a belly wood and hickory/bamboo for a backing. If you're aiming for a high draw weight bow, in my opinion getting quality wood for the back and belly is even more important.