After some research, I discovered that peel and stick wallpaper does best on smooth, untextured walls, and it doesn't hang on highly textured (popcorn) walls, but for orange peel walls, it just might.

Peel-and-stick wallpaper can be DIY’d and installed as a weekend project. Keep in mind, you’ll want to have a few supplies on hand, such as a measuring tape and a quality paper cutter — but ...

I've installed peel-and-stick wallpaper from Chasing Paper for many decorating projects. Here's what it's like to install and why I love it for rentals.