I use a lot of different kinds of glue. For collage I like to use wallpaper paste. It dries slowly, and I’m able to reposition pieces if I want to. Also, if you want to lift something after the paste dries, you can add water to the area, and in most cases you can lift the paper without damaging the surface or the paper piece.
After the paste dries you can draw or paint on it. Use regular wallpaper paste, the paste you use for borders is like a glue, and you aren’t able to draw on it easily.