The paper wraps all are pretty much alike.  Some are a little thicker than others.  You are correct in how to proceed.  Wrap all the way up to the bottom of the first branch.  This help protect against sunscald.  However, it does not protect from rabbits and mice who LOVE the sweet bark of fruit trees.  It would be good to purchase those plastic tubes which are sold at garden centers to put around the truck over the winter months.  They go on in October and off in March/April.  Critters cannot chew through them.  Here is a link about protecting your trees.  I personally have the hardware cloth in a circle a little way away from the trunk and leave it there all year around.  This time of year I put burlap on the outside to protect from sunscald and take that off in the spring. Open the drop down on Reducing Animal Damage: Protecting trees and shrubs in winter | UMN Extension