At the restaurant supply, I bought a few sizes of "crispers." They are hard plastic just likle the pull out ones in your fridge, and come in full size, then half, third, etc, kind of like buffet servers. Thing of the salad bar type things, with the plastic lid and a little opening for a serving tong to stick out.
I have a huge deep one, and then a few smaller ones. I measured my fridge so that I keep 3 of them on one big shelf (one huge, two half sizes). I put all my washed lettuce/greens in the huge one n(i eat lots of salad/spinch) with a damp paper towel on the top, then lid. In the others I just put all my other veggies, zukes, carrots, etc. In one usually fruits or whatever.
I also keep things in the crispers, but they don't hold a lot. This way, they are in something protective, away from things smooshing them in bags or something spilling on them.