I use soil. Outdoors right now, so nature takes care of the lighting for me. :-)
I use soil treated with fulvic/humic acid and watered with dilute ocean water as to super mineralize my crops. This also makes them disease and mold resistnant. I use plastic trays, with plastic lids.
After you slice the grass you can get one more smaller crop before it heads to the compost, which will eventually become soil again for future crops. (highly mineralized, healthy crops).
This forum has some very knowledgabel people in it. You have found a blessed place.
Are you going to grow barley as well? How about sprouts or rejuvelac, etc?