Moving a boat through the water with the least effort and most control is in your hands, if you're holding a paddle. To clarify terms, a paddle is a stick with a wide, flattened end used to propel a boat only while facing forward. An oar is a very similar shape but used only while facing backward. Rowboats use oars. Canoes, kayaks, paddleboards, rafts, and pirouges (to name a few) use paddles.
Traditional paddles of all types are made of wood. Warm to the touch, repairable, and potentially very pretty, wood is still a valid material for many paddlers, and can be found at many price points. Better paddles will use different woods for flex, stiffness, and weight savings while applying reinforcing fiberglass and epoxy to improve durability.
The most economical paddle construction is an aluminum shaft and plastic grip and blade. The plastic is durable and replaceable while the aluminum is lightweight and stiff. Composite shafts are becoming more affordable, but a cast resin blade will be consistent, since the material has just enough flex and durability that the paddle can be used as a pole when navigating shallow channels.
When speed and performance are what you want, the shaft and blade materials will be the lightest, stiffest material available - composite resin and Kevlar or similar high-strength fibers. Reducing swing weight means less exertion and a stiffer construction means better power transfer through the blade and into the water. That stiffness frequently may also have some brittleness, however, and at Kevlar prices, a broken blade will make anyone cry.
The ideal canoe paddle shaft length will be the distance from the water to your chin while sitting in the canoe. To get an approximate measurement, sit with your seat about 6" off the floor and measure the distance from your nose to the floor. Most canoe paddle blades are about 20" long, so add 20 to your measurement to get the overall paddle length you should be looking for. The most common sizes are in the 54" to 58" range.
A conventional canoe paddle blade is in the same axis as the shaft - the paddle is straight these are by far the more popular and versatile design. A 'bent' or racing paddle has an angled blade so the face is vertical in the water through more of the stroke. The shaft length will be shorter, anticipating the paddler will be bent closer to the water. The more time you spend in your canoe, the moer you will appreciate a bent paddle
For kayak paddles the sizing math is a bit different and the options very different. Whitewater kayaking needs high control and durability, so most whitewater paddles will be short (191 to 200cm), and heavy with a wide and very durable blade. They are also frequently a single piece shaft for strength.
Touring style paddles are used by most other kaykers, and expect a fairly regular cadence and mid-to-high stroke angle, so in general they will be longer (220-240cm) than whitewater but the blade size will be a bit smaller to reduce drag through the stroke and overall weight will be less. The two-piece shaft will break down for transport and allow the blades to be feathered.
Feathering rotates the blades out the same plane and can reduce wind resistance for the blade out of the water, but will also require more wrist action. Some amount of feathering is available on almost all two-piece paddles and is worth exploring to see what works best for you.
The grip section on better kayak paddles will have an oval shape to better fit the hand, and different shaft diameters may also be available for better comfort.
In open-water or sea kayaking, distance is the goal, and the paddler uses a high angle and a fast cadence, with a focus on minimizing weight and maximizing power. It is common to see all-composite paddles in the hands of long-distance paddlers. A distinctive element of high-end sea kayak paddles are bent sections at the grips for what is referred to as a 'crank' shaft. This can relieve stress and increase endurance.
Stand Up Paddleboarding
Very similar to a racing canoe paddle with an angled blade for steering and control, the shaft lengths run from 60 to 86 inches with a relatively small blade size and shape. Since the board has a shallow draft, you won't need much surface area to move fast.
Size selection will be based primarily on rider height - your paddle should be 4 to 6 inches taller than you are. Adjustable paddles are great for figuring out your preferred size or for sharing, but a fixed-length shaft will be much lighter.
To summarize, your paddle can make a nice day in a good boat great, or make you wonder why you left the house. Balance cost with perfomance, and you'll find what works best for you.
Shaft: Section of a paddle between grip and blade (canoes) or blade and blade (kayaks)
Blade: Wide, end of a paddle, can be flat (in canoe paddles) or curved (for kayaking)
Throat: Section of a paddle where the shaft meets the blade
Grip: Section of a paddle where it is held during use. In canoe paddles, specifically the end opposite the blade. In kayak paddles, sections equidistant from the center will have different material and a more oval shape the reduce fatigue.
Stroke Angle: Angle the paddle meets the water. For most canoe strokes, this will be 90 degrees. In kayaks, it will vary widely with the cockpit size and activity.
Cadence: Frequency and speed of paddle strokes. High cadence will move the bost faster but require shallower strokes to decrease resistance.