Wallpaper, unless under glass, is going to rapidly fail due to heat and moisture. Paint is longer lasting but, eventually, heat and moisture and scrubbing will take its toll, not just on the paint, but also on the wallboard underneath it. If you cook (more than just heating something up) wallpaper and paint just don't cut it even if one is diligent about using the vent hood.

I have had paint and wallpaper. The wall paper eventually failed, but it took over 10 years. I used vinyl paper and did not have to treat or seal it. Everything wiped off. Even tomato sauce.

I used semi gloss paint behind the stove and that wiped up easily.

I now have plain white subway tile. I like it also.

Any of those choices are viable alternatives.

Metals look good and are easy to clean as well as being fireproof - consider copper in all its variations, stainless, zinc, etc.

Glass is fantastic - easiest to keep clean, and you can paint behind it first, or put up an image, or have it printed on the back of the glass, etc.

If it's behind a stove then tempered might be a good idea!