To clarify: If you have GM staff, your Staff and Unarmed skills work together (assuming you have a staff equipped), but your Armsmaster skill doesn't work. At any level of staff below GM, you'll be using your Staff and Armsmaster skills, but not the Unarmed skill.

I did some testing long ago, which I barely remember now, and which established (I think) that you'll kill things faster if you spend your skill points in Unarmed and don't use a staff at all, than if you use the combined skills with a staff.