I think if you want to use the leaves small then anything from 2 inches is ok (as in a seed tray). If you want the plants to get to full size maybe 6 inches deep would be needed.

I think you can plant any salad leaf seeds around now for a crop in 4-8 weeks. Get some shallow containters - some garden centers sell long shallow troughs abour 4 inches deep with a tray. Fill with any kind of reasonable multi purpose compost, sprinkle the seeds on top (not too thicky), barely cover with some sieved compost, soak by standing in some water until the surface starts to appear damp, leave for a few days and then you can started to eat the thinnings! If they look too close together then they are so just remove some to leave more space. Keep well watered but not soaking. Protect from the absolute searing heat in midday on a hot day (who am I kidding!). Keep vaentilated during the day. Some varieties: oak leaf, lollo rosso, blenheim, rubane, osterley, exbury, bridgemere, baronet, antago, blackhawk, garrison, annapolis and roselee the list is almost endless and ther are "cut and come again" mixes you can buy from the garden center.

You could also try oriental leaves like Wong Bok, Pak Choi, Komatsuma, Shungiku etc. I am growing these at the moment.

There are also others like spinach, prepetual beet, endive, lambs lettuce, land cress.