not sure on any costs, really, but I think lights will probably run you any where between 500-1000 bucks, the soil and pots, fertilizer etc. defintely be had for under a hundred. (my parents garden like crazy so I had most of this shit lying around when I got started) the closet space sounds good for about four to six plants, any more then that and you'll probably stunt their growth. you'll also have to rig someting so the door closes or you'll have a hard time regulating temperature and humidity. run power through the wall via an extension cord unless your an electrition!! cover the inside in foil and make sure your lights can be lowered and risen.

If your serious about growing the first thing you should do is get a good book on the subject.