Tools for painting a wall
Given the texture of the wall, I'd try with just a 2-3 inch brush, one coat of primer, then two coat of the same exact paint as the rest of the wall. Ideally some leftover from the original painting.

Needless to say, let dry between coats and clean/dry your brush thoroughly. 
Edit: For cleaning the brush, run water over it until the water runs completely clear, then run some more water. Personally, I use a regular fork to comb the brush as I rinse.

You'll remove the hanger while you paint, right?