Hello eccentric,

Welcome to the boards.

When people refer to using a "filter" it is usually a charcoal filter and it would be located in your closet,connected to a fan that would draw air from the closet thru the charcoal and out of the closet. This would keep you from having to open your door for ventilation, you would just need a small passive intake. Which could simply be the crack under the closet door, as long as the fan is running a negative pressure in the closet keeps all outside air going into the closet and then out the filter.

Could not see exactly what seed was in your link, page I got showed it timed out, but any indica/sativa cross should work ok.

A 2'x2'x6' space could be ideal for one plant if you'd like to grow a small bush.

Floro lighting can be used, either CFLs or better would be T5 linear bulbs.
Keep in mind that 6500k (degrees kelvin) bulbs are best for veg and 2700-3000k bulbs are best for flowering.

A 2'x2' grow area is 4 sqft so by wattage you'd like at least 120-160 watts during veg and 200 watts or a little more during flowering.

Any inexpensive timer should work for you.

Hope this get's you a starting point and good luck.
OM