For a closet, I'd suggest T5, CFL, or LEDs for the grow to make heat management much easier.
You'll still want a ventilation fan, and an activated carbon filter for covering the smell, and if you can vent into an attic or right outside would be ideal, if not you can vent out into the room, but may need an air conditioner to control room temperatures at that point.
For a simple, bare minimum grow setup you'd be looking at about $100-$200 startup cost for all materials. But you can also expect that to reflect on yield.
If you can spend the extra $ for a HPS/MH grow light, and the appropriately sized fan to cool the area, you'll increase your yield.
LED grow lights have been doing amazing for several members here, but their initial cost is expensive, however you'll make that investment back in less power consumption for fans to cool the area, and power for the lights themselves.
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Everything you need to know