How do I prepare a wall for painting?

Why don’t you just remove it. You can go to your local tool rental shop and rent steamers to remove the wallpaper. Home Depot would probably have everything for the job. There is a tool that you run over the paper that puts little holes in it and there is also a product that you put on after that starts dissolving the glue, that cures for about 20 minutes, sometimes you don’t even need to steam the paper starts to peal off easily! That way you can paint properly and have a lasting job. Now you have a couple of solutions to chose from

I have painted over wallpaper, and that old fake wood paneling before with no problem. All I did was patch holes, reattach any spots that were loose, and prime. If there is any chance the wallpaper was put up with wallpaper paste, you may want to do a test area with primer and the paint to be sure it doesn’t dissolve the glue. Or talk to someone at the paint store for advice on best products avoid the issue.