No, a paddle strop is all that you need, a linen could keep your leather cleaner by stropping pre-leather, but a damp paper towel once a month or so will also keep it clean.

A paddle is the best way to go for someone new, as it eliminates the flatness issue that so many seem to have a problem with. If the strop is not flat from the spine to the edge, under the razor, the strop will roll over the edge and round or break it. A paddle eliminates this issue as long as lite pressure is used.

Always strop with lite pressures.

Paddles were very popular at the turn of the century, and are still an effective way to strop. 50-100 laps will keep you shaving very comfortably for a long time.