Use priority overnight, gauranteed delivery before noon. I like Fed Ex, Single coral box IE Med Pack box from Fed Ex around $5 w/ the outter bag will ship a coral up to 3 X 3 ". Shipping costs ~ $45 Need to pack coral in heat sealed bag or thcik double or triple lined LFS bag w/ good RB seal. As far as shipping temps go you must think about temps on the route of trip to destination. Say if shipping from Michagan to Texas check the weather at destination, you may need heat pack in Michagan but a chill pack in TX. But usually OK w/ chill packs. Better to over cool than to overheat. And a chill pac placed in at room temp can actually help keep a box from freezing and then cool on the warm side of the trip.
Placing bubble wrap inside of box sheild from cold and heat as well as bumps.
Good luck