I don't think the backsplash will be an issue at all. Where are you putting it? At the sink? I would think if it is something that could go in a kitchen than it could go into the laundry room.

More concerning is the laundry room on the 2nd floor. I have heard some that have had too much movement in their floors to successfully have washers upstairs, especially front loaders. Check the installation recommendations for your machine.

Maybe someone else with more knowledge with machines can weigh in.

Thanks enduring. I've done some research on the upper floor laundry rooms - I thought I saw some here who had solved that problem. I will do more investigating into those solutions and the best machines to get.

I'm glad you think the natural stone tile won't be a problem. DH is nervous about putting natural stone in the kitchen, so I was equally nervous about the laundry room. The backsplash will be behind the sink, yes.

You will want to seal the tile before you grout it, keeping it out of the grout spaces. Sealing the surface prior to grouting will help release the grout at clean up. Then seal again when finished. I have a marble backsplash in my kitchen and I have had no issues. I installed it in 2011.