You should have no problems doing 6 plants in a 4*4 for $700 if you live in an area where there are medical growers...if your in a state where medical use is not allowed, I am going to guess that finding quality used equipment is much harder to come by.
DIY hydro system, aeroponics, bubbleponics, drip feed, etc, can all be done for cheap. You could use 1 large rubbermaid as a a self contained resi/growing area, but if you have 4*4 you might consider throwing an additional unit in and bumping the total plants up to 12 if its not an issue. If you really want to absolutely fill that closet, you could just do 3 large sites each on two rubbermaid setups and grow some monsters. I'd budget no more than $100-150 for a DIY hydro setup.
600W is perfect for that size closet, but unless you can find a way to properly cool it, heat will be an issue. I just threw a 400W MH into my closet which is similarly sized, and it raises the temps a good 5 degrees in 10 mins when it fires up...Good news is you won't need a huge fan, couple hundred CFM's will do; if you can get a hood with air cooling hookups great, if not, you can get some high end computer fans which will move over 100 cfm, throw a few of those around the room and try to vent in some cool air while venting out the hot air around the lamp.
IDK how you could ever spend $800 on 6 plants in a 4*4. Keep it simple, gen hydro, adv. nutrients and maybe an additive or two along the way...shouldn't set you back more than $100 for the cycle, maybe a little more if those monsters are bigger than 3 feet.
Get liquid budget P.H. test kit, and take it easy with the nutes until you get a feel for the plants, then start bumping doses a little at a time.
It's also possible to grow some decent bud with CFL's and florescents, but HID is better if you can afford the power and can deal with the heat.
More important than all of this tho is planning and putting in a little elbow grease! Good luck