Picking a Paddle

Which paddle is the best is a hard question to answer. Hard, not because it's hard the pick one for a specific job, but because there are so many different things a paddle is called upon to do.
I'll make a basic asssumption and assume you aren't looking for advice about some of the more exotic, special purpose, paddles.
The 2 key things about chooseing a paddle are how it fits the paddler and how it fits the job at hand.

Shaft Length

The most important measurement in paddle fitting is the shaft length. There are plenty of rules-of-thumb for fitting paddles. Most don't work reliably because they assume a specific type or style of paddle. The one I use is simple. It give you the proper shaft length within an inch or two.
Stand facing a mirror and hold a paddle or broom handle over you head with both hands, thumbs facing inward. Bring it down towards your head till your upper arms are level and pointing straight away from your body. Then move your hands in or out till you forarms are vertical and make a 90 degree angle at the elbows. The distance from the outer edge of one hand to the outer edge of the other will be within an inch or 2 of the proper paddle shaft length from the top of the blade to the underside of the "T" grip. If the paddle you are looking at dosent have a "T" grip add an inch and measure from the top of the blade to the top of the grip. Only paddling with a paddle of a specific length will verify if you have it right, but this will get you very close on the first try.
Once you have the shaft length, take a tape measure and go out and buy a Mohawk or Carlisle brand "Cheepy" paddle. Both these brands are tough and on the heavy side. They will last years and become your backup and "beater" paddle, when you get a good one at a later date, once you are sure you have the shaft length right.

Shaft style

To bend or not to bend, that is the question. The functions of the bend in a bent shaft paddle are to move the power part of the stroke farther to the rear, for better ergonomics of the upper arms, for a paddle position closer to the centerline of the canoe in the stern seat and to stabilize the paddle by putting the force of the grip hand behind the verticle centerline of the paddle. Confused? let's break all that down.
The bulk of the work when paddling is done when the paddle blade is nearly perpendicular to the direction of the stroke. That means 7 inches before and after vertical on a forward power stroke. When useing a bent shaft paddle, that means that the shaft is past vertical when the blade is vertical. That puts your arms lower and in a slightly better position for mechanical advantage.
Because the shaft is past vertical, the blade is farther back and, at least for the stern paddler, can be positioned closer to the centerline of the canoe simply because the canoe is narrower nearer the ends. For the bow paddler the farther back the power portion of the stroke is moved, the farther out away from the centerline it has to be. Because a percentage of effort in paddling a canoe is keeping it going in the direction you want and the closer to the canoe's centerline you paddle, the less effort you waste on turning the canoe and then correcting for the turn.
The bend in the shaft also helps a tiny bit with paddle stability. Your shaft hand is behind the imaginary line between your grip hand and the center of the paddle blade. That combination is inherently stable and san help reduce fatigue. It's not much difference, but it is there.
Well you must be thinking, "Do I need one?". Probably not. If you have a narrow marathon racing canoe, a bent shaft will make a big difference. If not, the slight advantages will be offset by the disadvantages. In a typical whitwater or touring canoe, a bent shaft will put the bow paddler's power stroke too far out from the centerline of the canoe. The gain for the stern paddler will be offset by the restrictions on steering. A "thumb-up" "J" stroke works well but feels uncomfortable. A "thumb-down" "J" stroke dosen't work well at all. The angle between the shaft and blade confuses the instinctive simplicity of a high or low brace. It can be turned around so the back becomes the power face for a really good draw stroke. But, it takes a fraction of a second to turn it around. A normal draw stroke, started a fraction of a second earlier, will do just as much. It can help or hurt, but always takes more practice and mental effort to use it well. The bottom line is that it isn't worth the grief and extra expense unless you have racing or near-racing canoe where you can get the full benefit or will be paddling long distances on open water with little stearing.

Blade style

There are a myirad of blade styles on the market. Most of them, variations on a few basic theams.
Rounded rectangular is popular among whitewater enthusiasts. It allows a large blade area without excessive dimensions. These paddles typically have an aluminium shaft that extends most of the length of the blade. The thickness of the shaft affects this sort of paddles ability to make sculling style strokes, but that is not as important to whitewater paddlers as brute strength. The heavy construction and lack of finesse got these paddles the nickname of "War Clubs."
Another style you might see is an extreemely long narrow blade. These were used by Native Americans for hunting. The paddle is rarely lifted from the water. Instead, it is sculled silently, while the primitive hunter snuck up on streamside game. It's a handy paddle for bird watchers, photographers and hunters, but isn't particularly practical for general use.
Many of the lightest weight paddles are a cross between an teardrop and triangle. It's a very efficient shape and works especially well with a bent shaft. It dosen't translate well into the larger sized paddles, so it's usually only used with lightweight, highly efficient hull designs.
Rounded shouldered rectangular is a common and usefull design. It combines the area efficiency of the rectangular blades with a sloped shoulder that sheds weeds and allows it to be used in close to the hull.
My personal favorite is the beaver tail. The exact proportions can make it more usefull in a particular type of water, yet it still functions well in all conditions. Developed by Native americans to be the best all around paddle, under conditions where the usefullness of your tools could mean life or death, it has yet to be surpassed by modern technology. Specialty designs may surpass it in one area or another, but the Beavertail remains the best overall style.

Blade size

Size is slightly more important than shape. The bigger, heavier or less efficient your canoe is, the more square inches of blade you need. It's simply a matter of being able to get sufficient "grip" on the water for the canoe you are paddling. Too small and you might not be able to make a tight turn on a small creek or make it into that must-do eddy in whitewater. Too big and you waste effort with every stroke. Bigger cars have bigger tires. Bigger canoes with bigger loads need bigger paddle blades.
It's not rocket science, but the engineering principle of matching power source to load does apply. In this case, the shaft length matches you to the paddle. The grip style, shaft diameter and shaft cross-section optimizes your comfort and control. The blade area matches the paddle to the load being propelled. The blade shape optimizes the blade area to the conditions.

Materials

Wood was and still is one of the best choices for paddle construction. It allows smooth transition from shaft to blade and a fairly thin blade. Old growth Ash is probably the best, closely followed by some other hardwoods. New growth Ash, sometimes called soft Ash, works OK but is not as water restistant as old Growth Ash.
Laminated wood has several advantages. Because it allows smaller pieces of wood to be used there is less waste and the pieces with the best grain can be used. That allows some economy. It also means that the grain of each piece can be positioned to take advantage of it's inherent strenght. Laminated shafts and blades can be thinner and lighter than paddles carved out of a single piece. On the down side, all the advantages depend on the glue holding it together. Laminated beavertails should be avoided as the curved bottom seems to crack along the laminations. Laminated paddles are best with somewhat squared bottom and a tip guard. Laminated shafts allow for all sorts of curves and can go far beyond a simple bent shaft.
Aluminium works well as a shaft material in heavy duty paddles. It's strong and stiff. In many cases, too stiff. Paddle flex actually helps cushion your joints and can lessen fatigue. Nevertheless, aluminium, combined with plastic blades, remains a popular choice for both cost and durability. It works best in paddles with the shaft extending through most of the blade length, a design that is not condusive to finesse, but is good for strength.
Carbon fiber, Kevlar and Fiberglass are all used in paddle construction. Because of the expense of materials and labor to build paddles with these materials, they are usually only used in the construction of top end performance paddles. The rule of thumb is, with a few exceptions, if your canoe isn't made of Carbon, Kevlar or Glass you probably don't want a paddle made of these materials either. If you have the sort of high performance, lightweight canoe that can use a high-tech carbon fiber paddle to it's fullest, you probably don't need my advice on paddles.
Plastic works well as a blade material. It's cheap, durable and no-maintenance. As a shaft material it sucks. In a reasonabley thin shaft it has to be molded with thick walls, so it's heavy. If it's molded with thin walls it has to be a much larger diameter than is condusive to a good grip. Plastic works best as blades, grips and as a covering over an aluminium shaft.

Some Thoughts

For a first paddle I recomend a Standard Mohawk. It has a 19 inch blade, so just add 20 inches to the shaft length you determined useing the rule of thumb above for the paddle size. It's cheap, durable and adequate for basic paddling. It's the cheapest way to be sure of your shaft length. I use mine as a backup and as a beater paddle in places that would chew up my good beavertail.
Once you are sure of the shaft length, it's time to start looking for a paddle that fits you perfectly and suits your needs better than the Mohawk. Most likely, what suits you best will be a beavertail or a laminated paddle simmilar to a beavertail with a squared off bottom. Look for a thin blade that will slide easilly through the water edge first. Remember, the blade length dosen't matter in how it fits you. Generally a blade a bit longer and a bit narrower than the mohawk is a good all around proportion. Shorter blades help in shallow water. Longer blades give you a bit more control. As it gets shorter it should get wider to keep sufficient surface area.

Some More Thoughts

The standard Mohawk paddle, the bottom paddle in the top photo, has a 19 inch blade and a 1 inch thick grip. If you take the shaft length you figured out useing the instructions above and add 20 inches you will be very close to the right size for you. The Mohawk standard is designed to have adequate blade area for most uses, includeing some less-than-efficient canoes. It's upper blade shape is sloped just enough to shed weeds somewhat easilly. The squared off lower edge is durable and shortens the length compared to the equivalent bevertail. It's drawbacks are just as numerous The aluiminum shaft is cold in the winter. The plastic sleeve helps only a little. The aluminum dosen't contract as much as the plastic. That makes the grips come loose and the blades crack in freezing cold. The shaft extending through most of the blade disrupts the flow of water across the face of the blade. That really screws up the effectiveness of your strokes when using sculling strokes or any other stroke where the blade slides through the water edge first. Because many of the more advanced strokes that save you much effort include some amount of edge first paddling, you will waste a lot of energy over the years. It's still an excellent beginners paddle. I recomend getting it as your first paddle, or a pair of them if you will be paddling tandem. For a second paddle, get something better, something that will let you take full advantage of your skills and your canoe's capabilities. I suggest either a good laminated paddle with a simmilar blade shape to the Mohawk or even better, a hand carved beavertail made by someone that knows how to fit it to the paddler.