Hello Runna,
The first thing I would do is read this article, not because you shouldn't use the closet, but because it points out the difficulty in treating tiny rooms:
RealTraps - Vocal Booths
Generally, small rooms like that you want to make as dead as possible ... at ALL frequencies. Foam is useful for deadening at higher frequencies, but most acoustic foam isn't thick enough to help a lot with the bass.
If it were me, I'd put thick absorption on the ceiling, at least 4" if not 6", spaced down from the ceiling. You probably don't have room for 4" traps straddling the corners, so just use panels flush against the wall, as thick as you can make them.