It should be deep enough so that the potting mix becomes a loose Slurry in the pots or flats. This makes it very easy to put the seedling roots into the medium. A pencil or bamboo skewer or chopstick aids in the placement process, When the seedling have been planted, lift the pots or flats out of the solution and the mixture will sink to the just the right depth. I brought some plastic trays that have matching clear plastic covers, from Mellinger's. I keep the seedlings under fluorescent lights for the first 3 weeks.
Cheapest tubes are fine.
After the first week, I replace the original cover with one that has 6-half inch holes cut into the sides to provide ventilation. At the end of the second week, I replace with a cover which has half the top cut away. At the end of the third week, the seedlings are ready to be uncovered. I water carefully while the seedlings are in this seedling potting mixture. I dig down into the mix, and when it is dry half way down, I water.