Keep a nail brush and orangewood stick separate from your fingernail tools to avoid spreading bacteria.
The tip of an orangewood stick can be used to remove any remaining debris.
You may also want to use the rounded edge of the orangewood stick to push down the cuticles, just as you do your fingernails, especially if you plan on applying polish.
While all polish comes with its own brush, you may find you have better luck applying stripes or patterns with less traditional nail supplies, such as an orangewood stick, toothpick, or even a Q-tip with the cotton removed.