Considering that you are likely to paddle well over 1000 strokes an hour on an average canoe trip, which adds up to around 8,000 strokes per day or 56,000 strokes per week, the paddle that you're using has to be one of the most important decisions that you make. The problem is, it's not all that simple.
What you first have to think about is what type of trip you're going on. The route, whether it's simple lake paddling, navigating down difficult rapids, or a combination of both, is what you will use to choose out of the various blade styles. Each type is molded for the character of the canoeist as much as for the water course itself.
For general use, that being a trip that takes you from lake to lake, the old-fashioned Beaver Tail design works great. It's made from a solid piece of wood (usually maple, ash or cherry) and has a rounded end to it, like that of a beaver's tail. It's a great paddle to use for flat water tripping, especially at the bow.
For use in the stern, or especially solo paddling, the Otter tail is preferred. It's similar in design to that of the Beaver Tail but extended somewhat, has a narrower blade towards the tip, and has a shorter shaft length.
The grip on both the Beaver Tail and Otter Tail designs should be oval in shape and tapered slightly from the throat (where the blade reaches the shaft) to the grip. This makes the paddle far more comfortable and maximizes its strength than if had a rounded top. Just make sure that the long axis of the oval is perpendicular to the plane of the blade. If it's opposite to that, then the shaft will be very weak and most likely the paddle will break.
For whitewater paddling you need a much wider, square tipped blade to enable you to push lots of water in a real hurry. The previously mentioned touring blades are actually far more efficient when it comes to pushing water for the long term. Most of the blade length is under the surface and less friction occurs. The rounded tip also enters the water more easily. But to muscle your way across its far better to have a much bigger blade. It should also have reinforced tips to protect the paddle from sharp rocks. And for capital control the top of the paddle should have a T-grip. Avid whitewater enthusiasts also opt for synthetic paddles made from fiberglass, graphite, Kevlar, or plastic. They're tougher than wood, but are also ugly as sin and take away the whole mystique of paddling. A laminated softwood paddle works just as well if you look after it.
As for the new-age bent-shaft paddle, some canoeists love it, and some absolutely loathe the design. A canoe instructor I once paddled with is a faithful user of the bent-shaft. And being interested to see what all the fuss was about, I agreed to use one while out on the our trip together.
While out paddling the instructor explained to me how first-time canoeists automatically attempt to travel in a straight line by constantly switching their paddles from one side to another. Paddling with a bent-shaft allows that natural reaction, with the stern paddler hollering out the command "Hutt" to indicate the right moment for both paddlers to switch sides, allowing the canoe to stay on track.
He then displayed how at the end of a stroke with a straight paddle, water is pushed up to the surface, slowing your progress. When a bent-shaft paddle surfaces, the blade is vertical; no water is pushed up, no speed is lost, and less energy is used. This allows the canoeist to travel much faster with less energy.
By the end of the trip, having tried out the newfangled technique the entire time, it became obvious that the instructor was right with everything he had pointed out. We moved much faster en route and never once wandered aimlessly across the lake. The design made perfect sense. But it all honestly I couldn't stand it. I've never cared about how fast one goes while they're out there. With that kind of attitude you might as well stay home in my opinion. And every time he called out the command "Hutt" I went absolutely berserk - needless to say, we've never paddled together since.
How you hold your paddle is important. Make sure to keep your one hand always on top of the grip, which is why a nice rounded top is more comfortable than a T-grip. Your other hand grabs the throat of the shaft. The distance between your hand and the where the shaft joins the blade depends on the type of stroke and type of blade. When in doubt though, stay closer to the top of the blade for better control.
For trips that have both flat water and white water choose to bring along two different types of blades. After all, all canoes must be equipped with an extra paddle. So, when paddling solo use an Otter Tail most of the time and unpack the wide, square blade for navigating rapids. When paddling tandem, the stern paddler keeps using a Beaver Tail design throughout the trip, and, since the bow person is far more important while navigating through rapids, they can change over to the square blade when flushing through the rough stuff. Also try using a bent-shaft blade in the bow and a Otter Tail design in the stern when there's lots of big lakes to cross.
To size up your paddle is just as complicated as choosing the blade style. The traditional way to get the proper length of paddle was to line it up from your nose to toe. That doesn't work. The problem with this technique is that you are only interested in the length of the paddle between the grip and the throat of the shaft. The blade length is not part of the formula. It also does not take into account the kind of canoe you're using, the height of your seat, where you're seated (bow or stern), the length of your torso and arms, and the style of paddling you are used to.
The best way to measure the proper paddle length is to sit in your canoe and measure the distance from your nose to the water. You can also sit in the canoe while its in the backyard and just position the paddle beside you, upright and upside down. Then measure the distance from the lawn to your nose. Both approaches don't help when you're standing in the aisle of an outdoor store trying to pick out the right paddle. So, try this instead. Grip the paddle with one hand on the grip and the other at the throat (where the shaft meets the blade). Then place it over your head. If your arms are perpendicular to your elbows, then it fits. If your arms are bent outwards, then the paddle is too long. If your arms are bent inwards, then the paddle is too short.
Keep in mind that this is not a definite solution. For example, I prefer a longer shaft when solo paddling than when tandem. And in a difficult set of rapids I'd rather use a much shorter shaft than usual.