The o.p. indicates that he already procured one, viz:
The o.p. doesn’t say whether it is a sit-on-top or cockpit style kayak. If the former, he can forget the water pump and sponge, as sit-on-tops are self bailing. Since the o.p. says he’ll be paddling in lakes and slow moving rivers, I would assume that he won’t be far from shore and therefore doesn’t need a lot of protective gear, but a paddling jacket will provide protection from wind and spray, and a wetsuit if you’ll be paddling in cold water. A paddle float (for self-rescue) is necessary if you’ll be paddling alone in a cockpit-style craft, but sit-on-tops (and in calm conditions some wide cockpit craft) should be stable enough to climb aboard. If you are paddling by yourself you should carry a second paddle (paddle leashes are all well and good, but when you split a blade or break a shaft having a second paddle is a life saver). If you are paddling with others you should carry a tow line. Water (bottle securely attached in the cockpit or hydration pack attached to the PFD) is crucial. A compass, waterproof flashlight, and a dry bag with clothes and emergency supplies (food, medkit, matches, cell phone) is also a good idea if you are going on an all day trip, but if you’re just paddling in sight of shore and in clear weather they’re not necessary. If you are on navigable waterways you should also carry a marine radio, but I assume that the o.p. is paddling on isolated lakes and small rivers where this isn’t necessary. Oh, and the basic outdoor protective supplies, e.g. sunglasses (with keepers), sunblock, and hat.