You have determined that you want a sea-worthy craft, and it is between a canoe and a kayak. Decisions, decisions. There are some pretty obvious aspects like what size is preferable, what transport constraints are there (if any), how many people are going to be in the same vessel, what shape and materials it should be, and of course, and most broadly, What is the intended function going to be? For purposes of this article, I will talk about the broader differences and similarities of canoes and kayaks, rather than each in depth, for brevity's sake.
First things first, take in to account how you are going to store and transport your water-craft. Most canoes, palpably, are not going to mount onto a roof of a car or even fit into the bed of a truck. So if no trailer is available, a slim one or two person kayak mounted atop the car via either a secure foam-block or roof rack will do quite well. Furthermore, if even the roof is not a viable option, consider one of the high-quality inflatable or collapsible kayaks or canoes. Storing a reasonably sized canoe is sometimes a more attractive thing than storing a kayak. While kayaks are generally smaller and narrower, they need to be stored in more controlled conditions – many need to be kept out of direct sunlight and in a cooler environment, due to the polyurethane-based plastics commonly used that will not withstanding prolonged exposure. This is especially true of upper-end kayaks, which frames and finishes need extra-caution when in transport and in being stored.
This is how things work when the boat is actually doing "its thing" for lack of a better expression! From a storage standpoint, it should be more than obvious that a canoe is going to offer more. Offer more storage for people, as well as fishing equipment and so forth. Also, standing up to perform a range of activities is going to be significantly easier in the canoe, which will be a lot more stable anyways considering its broader hull. On the other hand, kayaks are meant for a lot more for speed, agility, and ease of paddling. Most canoes are pretty tolerable to even mild winds, and in worse conditions, it would be a miracle to paddle 10 feet ahead in a semi-straight line. The slimmer, lighter and more suitably-constructed kayaks will take winds and waves like a champ, though.
Safety concerns with both canoe and kayak are also very much worth mentioning. If you are considering buying a kayak, if for anything near extreme white water rafting, go for the one that does not "lock" you in via foot and thigh braces. Take it from me, you do not want to be upside down in a kayak and unable to get out of the cockpit! Of course, with a canoe, the advantage is obvious. Once you go shopping, if you go shopping with the canoe versus kayak debate, you will learn a great deal on the various models of each. In addition, you will get to see the vessel up close and personal, whereas pictures can only do them so much justice.