For CF, use kevlar string to bind the joints. If you will be using CA (fancy super glue, found at Hobby Lobby, and use the "medium" viscosity) 3M has a primer to use on the CF before wrapping and binding: helps the CA to adhere to the CF.
Deltaenterprizes: straight grain spruce is best. Clean grain bass is next best. Check with Aircraft Spruce and Specialty for "capstrip" stock. You can get it in multiple sizes. If you have good winds, and are making a fairly large kit, oh, say a 36 incher, 1/4" square stock is good, and you can make your sail from garden variety rip-stop nylon from your local fabric store.
Redhawk0: what you are describing is the Rogallo kite. Fun kites! Designed by a NASA engineer, by the way!