It’s possible to paint over wallpaper, but not preferable. The wallpaper seams will probably show through paint, and the paper may peel away from the wall. Vinyl wallpaper won’t hold paint, so that’s not an option in any case.
Your best solution is to remove the wallpaper and then paint the surface. Start by turning off the electrical power and removing outlet covers. Then score the paper with a special tool made for this purpose. This allows the wallpaper remover to penetrate. Spray a mixture of warm water and wallpaper remover on the wall and let it soak in. Then apply a second coat to moisten the paper and use a putty or drywall knife to peel it off. If the wallpaper-backing layer remains, repeat the process. Finally, patch any rough spots, smooth the wall with sandpaper, prime, and paint.