For milking in the shed I do have a stand the goat hops on and gets strapped in to eat while I milk (either machine or by hand). But not needed, just easier on my joints. Goats only needs tied up in theory, or not even that if she is placid enough.
I don't shear my goats (they are dairy), but for any sheep that I hand clip a couple of hurdles at right angles and the sheep tied up with halter, and then pushed up against one hurdle while I do one side, then switch over.