"I could tell you but it probably wouldn't be right" or some variant is usually my answer. The problem is not every paddler has the same boat, do the same things, are the same height and have the same financial resources. A few resources exist but usually it is a recommendation or a price point that causes a new kayak owner to buy the paddle they get.
Folks, this is the engine to your kayak! Please choose wisely or we might end up seeing you taking a bath on your purchase as it withers away on craigslist.org. Do you know how hard it is to recoup your money on a Pelican kayak on CL? Better luck in Vegas.
The paddle can make or break the experience but it is often thought of as, well, an afterthought.
I'll tackle a few tips and techniques for choosing a paddle here but the important thing is, go try one in the water. Places like Austin Canoe & Kayak have a demo day coming up September 15th. Go try one after you narrow it down. It will be well worth it.
This is done from a fisherman's perspective but can also apply to touring kayaks and general recreation.
Length: Paddle length is tricky but maybe this will help. Find a paddle at a shop and stand with it at your side vertically. Now reach up with one hand and curl your fingers around the top of the blade. If the paddle hits you in the palm, it's probably a bit short. If you can't reach the end, too tall. But hang on! Keep reading. Take into consideration the width of your kayak. If you are in a boat wider than 26" you need to bump up a size. Paddles are typically measured in centimeters and range from 210cm-240cm and usually by 10cm increments. At 6'2", I need a 230cm paddle, (monkey arms, I know), but I also paddle two wider kayaks at 31" and 36" so a 240cm is really best so I don't spend all day playing the drums on the side of my yak with my new paddle.
Blade Style: There are basically four categories of blades. You have wide and flat blades, narrow and flat blades, wide and scooped/winged blades, and narrow and scooped/winged. Variations are all over the board for these but two things are needed to decide properly. The wide blades are going to give you more power. They move more water and can allow you to turn faster, accelerate in choppy water better and fight the weather. These work great for fishermen because of their versatility. They also work better in wider boats, which are typically heavier and require more to move them. Narrow blades are more efficient. If you are paddling more than 2-3 miles in a day you might think about this option. Just understand if you are in a big, heavy, wide kayak, the advantage of the more efficient paddle is nullified. The decision about a flat blade versus scooped/winged blade is up to you. Sides are split as to added efficiency etc. I will say however that a flat blade is typically more durable for fishermen when used as an alternative to a push pole.
Material: Blades and shafts can be made of aluminum, plastic, carbon fiber, fiberglass, wood and a host of blends. Carbon fiber is lighter and can reduce weight for a long day on the water but if you are fishing oyster beds or rip rap it can make your paddle into splinters if you aren't careful. At this point let me say, I would recommend if you are buying a carbon fiber paddle, invest in a push pole or backup paddle so you don't cry when it breaks. And it will break if you abuse it. Aluminum and plastic are durable but usually heavy. These are also cheaper alternatives and what most folks will be using on the water. Nothing wrong with that! Just understand you will work harder throughout a day than you would with a carbon.
Weight: Since we are talking about it above let's continue here. Typical paddle weight is between 20-40oz. It doesn't seem like a ton of range but after a few thousands strokes, your shoulders and back will let you know the difference. I recommend the lightest, most durable paddle you can find for you situation. Durability and light are usually not synonymous so this is a decision that needs to be weighed carefully.
Cost: So many variables exist when you talk cost. All of the things mentioned above will play into it. Paddles range from $29 to infinity. There is a huge difference between that Academy $29 paddle and a $199 paddle from a name brand. There is much less difference between a $200 paddle and a $700 paddle as far as performance, materials etc go. The sweet spot for a very nice paddle is usually from $149-$229. This isn't in everyone's budget so buy accordingly.
Shaft Style: I won't spend much time on this but the new line of thinking is that a bent shaft puts less torque on the wrist and arms throughout the day, especially for inexperienced paddlers. A straight shaft works for most folks.
Brands: If you spend your time on the clearance aisle, some of these may be new to you. Check out the full line at places like Austin Canoe and Kayak, Colorado Kayak Supply and others. Some names you should know are Werner, Bending Branches, Aqua Bound, AT, and Carlisle.
That's about it. I've poured it all onto paper for you so now you just have to try one or twelve. Find a demo day and go. You can thank me later.