I want to add a light to a closet below a staircase (not a walk-in). What
are the codes related to this?

An old post I found mentioned there can be no exposed light bulb, and that
the fixture has to be 2 feet away from the rack or closer if using
florescent.

Considering code and ease of installation, what type of light fixture would
you recommend, and should I put it on the ceiling or the side wall?

Does the switch need to be outside the closet or can it be inside?

http://www.smugmug.com/gallery/849974
The light inside right now is a portable florescent I temporarily put on the
shelf.