Mike, if your building the stand with only 2x material, screws alone should suffice. If your using ply, I would definitely use wood glue. Elmer's or Gorilla would be fine. Depending on your joinery techniques, The glue bond will be stronger than nails or screws.
As for your picture, I don't know exactly what "washable school paste" is, but it does not look like it's meant for wood applications.