You said you would be growing in a closet. What are the dimensions? I would have to measure it, Im not there right now but it is a big closet.
You should grow your plants in individual pots. Pick the LARGEST sized pots that will fit in the space you have to use and still get adequate light. ok.
Do you have the ability to install an exhaust fan or will you have to rely on something like a regular fan blowing into the closet to move air and blow in fresh cool air and blow out hot air? I can not install an exhaust fan(live in an apartment) so I will need a fan or 2, where should I place them? This is another reason I was thinking about building something to grow them in.
Will you need a carbon filter? Well do you live somewhere where people might say what the heck is that odor and become suspicious and you might end up in trouble to some degree or another? If not you do not need a carbon filter and if you can set up an exhaust system that vents outside and there is no one near that will wonder where that odd odor is coming from and start snooping around you wouldnt need one either.
I would need a carbon filter.
You will need grow lights and you will get differing opinions here on what to go with but I would purchase a metal halide for vegging and a high pressure sodium for flowering. Others will likely tell you use CFLs.
Can I get those at lowes or home depot?
Nutes are nutrients, fertilizer.
You picked three plants. Did you buy feminized seeds or regular seeds? If you purchased regular seeds you may get three females and you may get three males and you may get one or two of either and one of the other but you wont know until you can sex them so if you bought regular seeds germinating three seeds may not give you anything and it may only give you a little and it may give you a half decent amount but it is a gamble if you have regular seeds instead of feminized seeds.
I bought regular seeds,I bought 10 seeds so I guess I will try my luck. If I get 3 males on my first try, should I scrap it and re plant new seeds or can I salvage it and still get some good from it?