ICE & a suitable cooler. While no expert on spear fishing as I am just getting started, I am and have been a fisherman for many years... Ice is imperative. Clean and ice your catch as soon as you are topside and done taking the pictures. Keep the quality of the fish pristine.
BUT, before you clean the fish, know the local laws. In NY and most other states, you cannot fillet or remove the head of a fish. Only gutting is allowed so that sizes may be confirmed (I think there is a provision for filleting but saving the racks, but that can get touchy).
Remember, many of the fish you catch or spear is likely to be much better than anything commercially caught as these fish are abused and borderline spoiled as they measure their catch by the tonnage, have faulty holds and may take a long time before the fish goes to processing.
Enjoy!