The problem with stacking is it limits what you can grow. Your teacher probably has space constraints which is why she/he is doing it. You will probably need to drill holes near the top sides of your container so the plant will be ventilated; otherwise you will have a terrarium.
Is your method of growth aquaponic or hydroponic? If it is hydroponic, drainage holes will be needed. If aquaponic, a possibility is a float system with lettuce. The containers will need to be tall, however, to allow for the size of the lettuce. If hydroponic, you could use a media, & grow low lying plants, such as radishes, some sedums, or salvia columbarie (chia sage). The chia can be later transplanted, taken home, & brought to the flowering stage.

Lettuce - 35 days to harvestable baby greens, 45-60 days to full size
Arugula - 21 days to harvestable baby greens
Basil - 6-8 weeks to first harvest.

There are already a number of hydroponic stacked growers on the market. Check out Vertigro and Hydro-Stacker.

I am wanting to start a aquaponic system for a small enclosed grow room, can anyone with experience give me an idea on the cheapest way to set one of these up?