Paddles are in some ways more important than canoes. I would rather paddle a bad canoe with a good paddle than paddle a good canoe with a bad paddle. The best tool for the job depends on the job at hand. There are river paddles, cruising, and touring paddles, all around paddles. If you don't know what kind of paddle you need than you probably don't canoe very often. Probably a few times per summer at the cottage or something like that. If this is the case get yourself a Beavertail or an Ottertail paddle, you just can't go wrong with them.

 The next question is wood or synthetic? If you are a traditional canoeist the answer is wood so that leaves the cheap plastic paddles for the rental places and the expensive synthetic paddles to Olympic athletes, and show offs with more money than brains. The synthetic paddles used by canoe rental companies are ugly but necessary in that business because they are tough and reasonably cheap to replace. Some people really like the synthetic carbon fiber and bent shaft paddles for going in a straight line very fast too. Nothing wrong with that if that is what you are into but I like a lot more versatility in a paddle so I don't have much use for them.

Wooden paddles come in all different configurations. Once you figure out the blade style you are going to use you will have to pick a type of wood for your paddle.

• What I can tell you from experience is that ash is best all around compromise. It has a good strength to weight ratio and can be made into a fairly light paddle but it will never be feather light. If looked after it is almost indestructible.
• Maple is tough, fairly light for what it is, but can be prone to splits at the tip; It makes a good working mans paddle.
• Walnut and cherry while beautiful, crack and break under great stress. I have seen both shear off under stress and break in the strangest of places. While some people espouse the virtues of cherry I would be very wary of an off the shelf cherry paddle.
• Poplar paddles wear out fast and cracks easy. They are however dirt cheap and available at department stores that carry sporting goods. 
• Softwoods like cedar, spruce, and basswood (actually a hardwood) make beautiful light paddles but will get beat up and need a lot of maintenance.

In general if you are wilderness tripping go with ash it simply cannot be beat. There is always the possibility of delamination of the grain with ash if it takes a beating and water gets in but any competent paddler will look after the tools of the trade on a trip. If the end is getting beaten up a bit it can be sealed with cooking oil, pine tar, or spruce gum. Maple is a good tough beater paddle if you are fishing by canoe and not one to take care of your paddles too often, while walnut and cherry are good for show paddles, but don't go too far from home with them unless you are completely confident with them.

The final thing to consider with a wooden paddle is the finish. Will it be oil or varnish? That is an easy one too. Varnish will give you blisters and oil will not. Oiled paddles need to be recoated every three months or so, but look beautiful. Varnished paddles only need to be touched up every year or so but once the water gets in, if left un maintained, its game over. If you want a maintenance free paddle, you may as well buy a synthetic one because all wooden paddles require a bit of sanding and sealing from time to time. If you want a comfortable beautiful paddle however, go with a solid wood paddle with an oiled finish.

Length of paddle and blade and grip type are a personal choice. I like a shorter paddle for solo canoeing and in the bow seat, but like a paddle that is a few inches longer for leverage when paddling doubles in the stern. In general longer thin blades are not as tiring as short wide ones but are less efficient for overall power. When sizing a new paddle the main measurement to be concerned with is the shaft length, If the shaft length is comfortable the length of the blade shouldn't matter so long as it is within reason. Just remember paddles are specialized tools and different tools perform different jobs

Short Wider blades like Whitewater paddles, Sugar Island paddles, and the like are best used on rivers while long narrow paddles like the Ottertail and Algonquin style paddles are best used on lakes. Paddles such as the Beavertail are often found on both lakes and rivers as they are a more generalized blade.