First grow, should I construct my own grow area or use a grow box? Pics inside

Hi, I am a first time grower with about a $1000 budget (I'd like to spend less than that but I can spend up to that amount). I have a closet in my house that I lease, and I was wondering if you guys could critique it on its ability to house a grow room. The shelving and everything is easily removed so keep that in mind.
Closet - Imgur

On the other hand, I may have to move out in around 7 months so should I consider gettings a grow tent? I was looking at Secret Jardin Dark Twin DR90T - Greners.com because I definitely want to have a continuous cycle of flowing and veg plants. I'm highly considering this tent. I like the 2 part option in this particular tent.

If I choose to construct my own grow area in the closet, how should I go about air intake and outtake? I can't really install a vent to go outside since I don't own the place... should I build a closet within this closet so I can have an environment where the air filters out some way? I can keep the closet open most of the time so it gets fresh air from our living room also...

Also, here is my current shopping cart, I know there isnt any nutrients or filters in there so can y'all recommend me a good affordable carbon filter and air systems and nutrients? Is that all I need for the lights or am I missing something? What else am I missing thats essential? (besides pots and chains etc)
http://i.imgur.com/fIlDl.png