How should the feeder wires to a subpanel from the main panel ideally be protected?

Sub panel feeder wires are run just the same as any of the circuit wiring in the house. The sub panel is just another load circuit. Make sure that the correct wire sizing is done to feed the sub panel. It can be run behind wall board. If run on the bottom of the floor joists it is best to nail a board to the underside of the joists and then staple or strap the cable to it. If it is below the five foot level from floor grade and on the surface it must be mechanically protected until it rises above the five foot level.