A bit of discipline when packing the puppets and props away will save time later when they are next needed and developing a 'routine' of what goes in first etc is also useful as if there is an established order it's easier to spot that one character has gone astray, and avoids unpacking thinking 'I don't remember seeing the monkey'
As for protection, heads folded into costumes go a long way to protect faces, but in these days of ever cheaper clothes we discard things regularly and I find the sleeves of fleece jackets make really good puppet bags.
They come in pairs of course, so help in establishing an order and connection between puppets. With mine, Judy and the Croc go into green arms, as the Croc is green and my Judy's dress is also green, they are also what frightens my Punch. My two policemen go into the blue sleeves, and the Devil and Clown in the grey sleeves as they both evil.
My final bit of the packing ritual , I'm sure many will also do, is once the last thing is in the car, is to return to the pitch and say to myself as I look at the ground , 'Right what have I left behind?'