Summarize:

If you are a fisherman, you need to start thinking about flavor preservation and storage temperature as soon as you get the fish into your boat. You have two options for maximum freshness. First, you can keep the fish alive in a live tank well onboard your boat and deal with the rest when you get back to shore.  The second option is to immediately kill the fish and put it into an insulated bin filled with a little water and a lot of ice.  Make sure to buy an insulated cooler with a drain plug. The fish needs to stay as cold as possible while in the cooler. Open the drain plug on the insulated cooler open so that melted ice water slowly and continuously drains out, making room for new ice. Do not allow dead fish to sit in melted ice water, because this will spoil the taste.  If possible, use shaved ice in the cooler. Position the fish down into the ice in the same position which they swim, bellies down. Surround their bodies completely with ice. Cleaning the fish as soon as possible will preserve the most flavor. However, if you're out for a day of fishing, you probably won't be able to clean the fish right away. You can hold off on fully cleaning the fish for a few hours (as long as they're kept on ice) but you need to remove the gills and stomach cavities from the fish as soon as you possibly can.  Their gills and stomachs contain waste, and you need to remove that quickly to avoid spoiling the flavor of the meat. Removing these parts also allows you to pack the empty cavities with ice, so you can keep the fish even colder. As long as they remain in a chilly bin and on frequently replenished ice, you can store whole fish for up to one day before cleaning them and still maintain flavor and freshness. Keep the stomach and gill areas packed with shaved ice. Be sure to keep them positioned upright, in the same position in which they would swim. This will allow the fish to easily drain any excess fluid out of the cavities. Cover the fish with more ice and close the cooler.  The fish won't be slimy when you take them out to clean them, because they've been kept on well-drained and frequently replenished ice. This makes them easier to handle. There won't be a strong or unpleasant fishy odor when you take them out to clean them. Cutting and slicing the meat will be easier, too.
Fill an insulated cooler with water and ice. Add ice to and drain water from the cooler regularly. Remove the gills and stomachs as soon as you can. Clean the fish within 24 hours of catching it.