Really, if your chuck jaws are not buggered with any burrs, you can wipe them down with a clean rag, msking sure there are NO chips on the jaw faces, and clamp the bbl in them tightly without marking the barrel. Marks come from two things: high spots (burrs and debris) or movement. Clamp the crap out of it and you should be fine. You DO NOT want to use (rubber, leather, cloth, etc) as you will not be able to clamp it rigidly, or it clamp it true. You're better off "steel to steel".
You "can" use thin brass shim stock (0.020 or so) but you might reconsider this.
At the point where the action sticks out of the headstock, the bbl should be rigid enough to not need more than a rag stuffed into the back of the spindle to keep things ok. Moderate turning speed unless you want to dynamically balance the entire thing. You can set up a lot of vibration as the action puts asymmetrical mass on the rotating assembly. Just take your time.