Most LFS have plenty of supplies you could purchase from them. If not then look at U-LINE supplies. They typically have everything needed for any sort of shipping needs.
U-line is a great place but you have to order in bulk. Their smallest carton count you can buy is 4. Unless you need larger then carton count for boxes goes to 2. They do not have heat packs. I usually buy my online. The 40 hour variety, you do not know if they could be held up in shipping.
Depending on how far it's going, I kinda like they way Ryan does it. Get some of the foam board from lowes/home depot, and cut it to fit the inside of a box. All 6 sides... Cheap & effective!
I ship to all of the 48 continental states, and I only use a sealed insulated container. I lose about 1% of my coral during shipping. To me it is worth the cost of the cooler. I also have seen boxes I have shipped coral in at frag swaps. Past customers use them as their coolers. Ben used one of my boxes at the last meet. But in this hobby as always everyone has an opinion, or something that works for them. So whatever works do it.
I'm shipping coral for the first time. It's going from here to Illinois. I need an insulated box or cheap cooler, heat pack, and bag large enough to hold the rock. Also, some way to keep the rock moist (considering possibly non-bleached paper towels with a half bag of water).
You shipping a very large rock? The larger the rock the more bags I use. Have you seen how shippers handle boxes? The first drop and a rock will go through a bag. Unless the box has a plastic liner then all of the water ruins the structure of the box and coral dies.
Any rock I've seen shipped is shipped "damp", not wet. Basically they're wrapped in wet newspaper & stuffed in bags & boxes. There is ALWAYS die-off on shipping liverock. But Spike would definitely know more about what works since he does this regularly.