Any hard hardwood will work, assuming you are not putting the handles under
extreme stress, like shovels. But I have even made shovel handles out of
alder, which is not very hard, which held up very well because they were not
cut with diagonal grain, like some handles from handle factories. A place
where several branches took off made a nice end knob for the top. I made
the shovel handles with a drawknife, not on the lathe.

Epoxy works great for fixing many types of heads. I buy a 16 oz epoxy batch
at a time and use it on a number of projects. If on a garden tool, it is
good to use a large diameter screw.

On lathe tools, a ferule (or reinforcement ring) is good to use. You can
use copper pipe, a brass bushing or other non-corrosive type of metal for
the ring.

Derek