For fingerpicking it is common practice (and most desirable) to grow your right hand fingernails. This will give you a greater control over the volume and tone of the notes you play.
The desired length of fingernails varies from player to player, however, as a general guide, the nail should be at least 1/16" (one millimeter) clear of the fingertip (most people prefer the thumb nail to be slightly longer).
Fingernails should be shaped so that they have a rounded edge, e.g.:
Fingernails should be filed and shaped regularly, working from the underside of the nail.