George, you could use 3/4″ stock if you want. I think Paul may even have said so in the video. There is nothing magic about 1″, but it will be a bit stiffer than 3/4″. As far as species is concerned, you could use a chunk of 2×6 if you wanted. There is nothing magic about beech. A hardwood will last longer and a softwood will scratch easier. But the wood you use makes little difference. Just get out there and use something and don’t get paralyzed by the details. If you find after some months of using your router plane that you might have liked to make it from something else, then make another. You’ll already have the hardware.
Matt, Northern California - Started a blog in 2016: http://tinyshopww.blogspot.com/