If the top section of vine is producing upper pitchers it will continue to produce upper pitchers after it roots. IF you root a middle section and a new growth forms from one of the leaf nodes it may have lower pitchers or uppers. It may form a rosette but if it does it usually starts to climb fairly soon and produce uppers again.
If there are not basal shoots growing you should always leave some green healthy leaves on the lower section even if this means they are way out on the end of a long brown woody leafless stem. If there are basal shoots you can cut all the way back to the basal shoots.
As for cutting leaves on the cut section. I cut them down anywhere from removing the pitcher to cutting the leaf down in length. This is to help me pot the cuttings and fit them in big ziplocks during the rooting process. Cutting back the leaves can help keep the cuttings from drying out by reducing the leaf surface area where moisture will transpire from. However the auxin (to promote root growth) is produced in the leaves. One of the reasons I usually dip in a little rooting powder although it's not absolutely necessary.