To store the fish you catch, collapsible wire fish baskets can be used since they will not occupy a lot of your space. Net fish baskets can also be used to store the fish you catch on a Kayak. To keep the fish alive, and if you intend to release it later, you might need coolers with oxygenated water to keep the fish alive.
However, if you intend to eat the fish and not release it, use a stringer. A fish can still stay alive on a stringer for as long as 3 hours, but the stringer injures the fish when it tries to struggle, so it is better to use alternative options.