I take a 15 gallon (swimming pool chlorine bucket) that has a water proof screw on lid - drill two 3/4" holes in the side and install a boat style live well pump outside the bucket with a detachable cigaret lighter power cord - we can transport bait to & from the surf or boat and carry it in the suburban without worrying about spilling it
5 Gallon bucket, aerator. We try to keep the bucket in the shade and will most of the time throw a frozen 20 oz soda bottle in there at some point during the day. I will bring them inside overnight and use a cheap aquarium pump once I have electricity.
I fish with croaker alot in the surf. All I do is put them in one of those big 15 gallon plastic laundry baskets/storage bin deals and put an little cheap $20 aerator. If its really hot I will put some frozen water bottles in there. Have kept croaker and shrimp alive for 2 days that way.