The glue we recommend is the Urea Resin type. That's what we use in the video. It's a powder which is mixed with water, and which is water-clean-up until it hardens. While it no longer is called waterproof (it used to be called this, but the standard has changed), it's far more waterproof than we need for our boats. It doesn't pass the boiled-joint test; don't put your boat in boiling water if you use this glue. This kind of glue is also called Plastic Resin Glue. You can find it at ACE Hardware stores; they can order tubs of their house brand glue if it's not in stock. You can find the Weldwood Plastic Resin glue online at Aircraft Spruce & Specialty.
Another glue people have used is the Urethane type. Different from the Urea-type above. These come in a squeeze bottle. It's messy, but it's strong. Look for brands like Gorilla Glue and such. These glues will work fine. Some people are allergic to the urethanes, so watch out for this.
Another choice is epoxy resin. This also works fine, and can be used to do the fiberglassing also. As with the urethane glue, epoxy can be allergenic so keep an eye out for this reaction. There's a school of thought which claims that the only type of glue to use for boatbuilding is epoxy. As with any extremist belief-system, it's not true. Epoxy is great, but any of these three glue types will work fineuse what you like!