Answer: Many states have restrictions on this, so first of all you should check with the post office and state agriculture departments to see if you can legally mail/transport the plants. As far as packaging, most commercial shippers send bare root plants (sometimes wrapped in newspaper) or small plants in small containers, or small plants with their rootballs in plastic wrap or small plastic bag, in part to reduce the weight and also to reduce the mess of soil getting loose inside the package. When small containers are used they sometimes place the pot inside a plastic bag while leaving the top of the plant unwrapped, or they wedge the pots in the box so they remain upright. Some shippers simply place the plants in the box and surround them with ample cushioning of styrofoam peanuts so that the box is filled. This keeps them from bouncing around.
The biggest problem may be heat if you are shipping them now -- it would be better to wait until the weather cools down in September if you can. That would also be a better time for transplanting.
I have moved and left extensive gardens behind several times and I understand how wrenching it can be. But also keep in mind as you do this that sometimes it is easier and less expensive to purchase replacements -- you can do so at a convenient time and a good time for planting and be assured of healthy starts that have not been stressed by handling and shipping and multiple moves. Your new property may or may not be well suited to the plants you are growing now, and you may find that your design goals change when you move to a new site. Every new garden is full of opportunity. Best of luck with your move.
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