First and foremost, always put safety first! If you have to skimp on something, make it something other than the precautions you take to ensure your safety.
You should have an adequate amount of clothing, a whistle, an extra paddle, and a lifejacket as a bare minimum. It is also essential to bring a change of clothes with you so that if you get wet while paddling your kayak, you can put on some dry and warm clothing.
The lifejacket should not require an explanation. Make sure that it can support your weight, that it is not out of date, and that it fits you properly before you purchase it. If there is one thing you want to avoid at all costs, it is going swimming and then losing your life jacket.
If your paddle breaks, the backup paddle will come in very handy. Because it is possible, it is best to get ready for the worst-case scenario. If you don't have a paddle, you will be floating around in a life raft. Bring along an additional paddle.
If you need to signal for assistance or draw the attention of another boater, a whistle can come in very handy. If you are in danger of being run over by a boat or if you require assistance in any way, blowing your whistle will get you a long way.