How do I choose an inexpensive backsplash for our mobile home?

You can try the glass gem backsplash idea! https://www.youtube.com/watch?v=Elny3HHSeeM

This collection might help you with ideas:

https://www.hometalk.com/diy/tile/backsplash/s-15-diy-subway-tiles-projects-41976054?se=fol_new-20190320-3&utm_medium=fol_new&utm_source=email&date=20190320&tk=hmxhqu&slg=e360981cd55f26467a71e7d988741b2d-bcabfcc3d5fb9ed1c228ea19b846597a39369a3ed007d424ed35ed56b3da86d4-2944783&post_position=12

My bff did a sticky backsplash in her laundry room and it was soooo cute and very inexpensive. here is a link to the stuff she used: https://amzn.to/2FjClFj

Yes theres something akin to contact paper on the mobile home wall panels.

You’ll need to double clean the walls first: try TSP solution and then when you think it’s all been removed, the next day wipe it down with alcohol.

If you want to lightly block sand it before priming with a binding/stain blocking primer, then you’ll need to alcohol wipe it again.

I would cut peel and stick vinyl flooring into ceramic tile shapes. Burnish then down.