It's just a question of what you want to see there. Formica is a good choice, but if you like the look of tile, you can apply a sealer especially made for the grout. The same goes for the floor.
I have done a tile back splash in my kitchen and a bathroom, and really enjoyed doing it. Designing with tile is a lot like quilting, but more people are impressed. I spent about $40 on a wet saw for cutting the tiles, but you might be able to rent one. It's extremely messy to use, so if you don't have an outdoor area and good weather, I wouldn't recommend it. I wound up wrapping a vinyl tablecloth around myself while using the saw to avoid getting soaked. Tiles can be cut by scoring and snapping, but I found that a lot more challenging when I tried it.
No matter what you put up there, if you have a texture on that existing wall behind the stove, it will probably be necessary to sand it all off. If the house is older than 1978 there may be lead paint, and sanding is not a do-it-yourself proposition. Even if lead isn't an issue, it makes an incredible amount of fine dust.
Formica is applied with a contact cement. You spread it on the Formica and on the wall and let it set up, and then you have to position the material exactly right on the first try because you can't move it at all. Tile is actually easier to do, IMO, and much more creative. For example, you could do a mosaic or a pattern from a quilt design. I'm sure you can find online tutorials and videos for how to do either tile or Formica. You could also do a Google image search for "back splash" and find some inspiring pictures.
Now here's another idea that I recently saw in a friend's house. You can buy molded pvc ceiling tiles that look like Victorian tin ceilings, or for that small area, maybe you could find the real thing somewhere. The big plus to using that is that it can be hung over the existing wall with no preparation. It's really cool looking stuff and can be painted any way you like. Give it a coat of polyurethane so that you can easily wipe it clean.