What material is best for cast iron handle covers?
I would go with silicone or leather. I used fabric mitts before and the one I used became brittle with the heat.

If you can "obtain" a silicone sleeve for the handle, that would save you the effort of putting on mitts every time you need to handle it. Test the silicone before you purchase it by putting a fire to it. If it burns, it's not real pure silicone.

Good luck!