Lets see...carry the...decimal here...

So about 16" x 21" x 30ish ANS (American Nonsensical Standard)
Sounds more like a shelf in a closet, lol.

Depends on the size of the pot. You can fit however many will fit, lol.

6-1 gallon pots, or 2 to 4 - 2 gallon pots, or 2-3 gallon pots, or 1 - 5 gallon pot (or larger) The larger the pot, tho...the higher the plant will sit. (takes away from headroom)
With limited headroom, you'll have to decide whether you want more headroom for a maturing plant (permenant in the closet) or more soil capacity. (definatelly going to move soon)
If planning on moving them soon, not likely an issue.
If seeds are not in the ground yet, start them in little "kegger cups" (cheap plastic cups with holes cut in the bottom for adequate drainage Often found at beer keg parties) or a similarly sized cup. They'll be in those cups for at least a few weeks, till rootbound.

Whatever you do, you'll have to keep in mind that you'll need ventilation and a fan on 'em.