Bubble wrap is a good key to protect painted minis. On my side when I ship a bunch of painted minis, I don't put them all in the big box. I use smaller boxes to compartment the minis (~size of the small E:40K infantery). Put some bubble wrap sheet all around the small box and put the infantery minis inside, add some bubble wrap over (there sould be some on each side of the box). You can make several layers

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For painted wehicules, bubble wrap each one and use some adhesive around to keep the proctection in place. If you have a lot of painted vehicules, separate them in small boxes and if there's too much room in the box, put some paper/bubble wrap to block the minis. Once all the small boxes of minis are done, put them all in a bigger box and one more time put some bubble wrap to avoid boxes from moving inside the big one. Less they can move, more they are protected.
I always consider that the post office employees will foot kick the box several time during the shipping so...I use a lot of protection and some strong (large brown one) adhesive to close the box. I have received a box that was closed by small transparent adhesive, adhesive did not suppport the shipping and when I opened the box, some minis were missing.