I've gotten a few packages shipped from Sexy Corals, thecoralfarmer and Rare Reef, I would just copy what they do, they all were packaged very similar
Use the minimal amount of water per coral
single bag each item then knot the bag
place 4-6 single bagged items in a bag and knot it then triple bag it each with there own knot
Take box lined with styrofoam or use a styrofoam shipping box and loosely pack with newspaper
place the coral bundles in box and fill with enough newspaper to make sure corals don't move
Before shipping you should check the weather, both where it's being shipped and where the item is actually going. For instance if you ship FedEx, the hub is in Tenessee, if the weather is 60degrees in the place your shipping to and 20degrees in Tenessee then theres a high probability that the package will be delayed because of the weather so a different day should be picked. This happened to my Sex Corals package, it took two months to get shipped because of the weather.
Anyway, for shipping and packaging supplies theres a store in Gibsonton that sells the plastic bags and styrofoam boxes for pretty cheap. Place is called 4fish stuff. Also, if you ship using ShipNEX the rates are much cheaper but I haven't used them. I've heard reviews of people shipping internationally and being charged hidden fees while people that use it for within 48 contigous states overnight shipping and don't have any issues at all. Another option is USPS overnight but have also heard they have the most delays and could lead to issues. Best bet is to use FedEX, it's what all the major coral vendor use. Hope I helped or offered some insight, good luck.