Just about any wood works well. My first one was with yellow pine and works great. Pine is heavy but you can thin it out to lower the swing weight. The paddle I just finished is western red cedar. Cedar is the lightest strength/weight wood out there but dents pretty easily....which I don't care. Grab a 2x4 you have on hand and cut away anything that doesn't look like a paddle.
Trust me, thin kayak blades are what you want on the carbon/glass/plastic store-bought paddles. I made my cedar paddle blades about 3/8" thick at the tips but its quite light weight and springy. The pine paddles worked out to about 1/4" but are probably 1/3rd heavier than the cedar. I use a skill saw, jigsaw, and power planner to get things close, then to a belt and orbital sander. I don't like 'shoulders' on the loom, just nice smooth curves. Spar urethane or tung oil for the finish only 2-3 coats. Sand no smoother than 220 grit....a little roughness seems to be easier on the hands.
Follow the directions in the link above and you can't go wrong, which includes measurements to fit you.
Here are some beauties! (mine all about function)
http://www.fridayharborpaddles.com/

http://www.google.com/images?q=greenland...ved=0CEAQsAQwBQ