Our closets are similar in size. Mine is a little bit deeper, not much. Mine is the typical apartment closet w/ a shelf on top.
Before I got a separate cabinet to veg in, i vegged and flowered in the same closet. I sealed off the shelf area on top and used that to root my clones and keep the mothers.
I ran a 150 watt HPS in the bottom for flowering.
I just upgraded to an aircooled 400 watt HPS for flowering. The 150 is Ok if you just wanna run a couple small plants, but I needed/wanted more than just a few small plants.
If you use a 150 no need to worry much about cooling, anything bigger and Id invest the few extra $ for a cooltube or aircooled hood.
Research cloning and perpetual growing if you wanna have plants constantly growing and being harvested. It can be done in a small space and I think its really the best way to use such a small area.