How to choose a backsplash for behind my stove?

These are mainly tile: https://www.pinterest.com/kitchenideas/backsplash-ideas/

I especially like #6 (textured tile): https://www.thespruce.com/kitchen-backsplashes-that-are-not-subway-tile-4142970

This is not your typical tile back splash: https://www.familyhandyman.com/kitchen/12-awesome-backsplashes-that-arent-tile/

I've used a sheet if stainless steel before

Last year we put a new back splash in our kitchen. And I love it. The tile came on netting with self adhesive. Very easy to install. The tiles are long and very slim. We grouted it ourselves too. Very happy with end result.

I would stick with a smooth surface because of grease and food splatters. My sister used metal flashing and it looks great. We have a large piece of stainless steel behind ours at the farmhouse and formica at our home in town.