People have done all kinds of things. I would do what is best for you and that probably does not involve grout.

I had granite tile but I didn't have a grill or do much greasy cooking. I don't care for the look of stainless or cleaning it. I guess you have to decide what's most important to you - function and what is most appealing to you or following the latest trend.

Another option that seems to be popular is glass and or back painted glass . Very easy to clean .

If it makes a difference, the new grouts are much much easier to keep clean.

I don't find tile a hassle now that I have a real range hood. I think stainless is a great choice - we thought about it but it just didn't go with our kitchen. In a more modern kitchen no problem! I wouldn't worry about what is in style.

also, before I remodeled I had flat paint by the range so tile seems like a breeze comparatively! Haha. I still can't figure out how to clean flat paint for the life of me.

We have the stainless high backguard with shelf. I also like taking the counter material up for the backsplash (if it is an appropriate material). Good luck!

we did full height granite on our cooktop wall... best decision ever!! no grout and super easy to clean

I'm a huge fan of stainless steel. In my old kitchen, DH installed brushed stainless steel behind the stove, all the way to the ceiling. It was so much easier than the painted wall to keep clean. And the rest of the kitchen was original 1952 vintage (i.e., yucky). However, in my new kitchen, I had white subway tile installed in a basketweave pattern and still thought I wanted a stainless steel backsplash. I bought a 28" high piece and the contractor installed it over the stove. In the process he made a horrible dent in it and tried to tell me it was that way out of the box (a lie, because I took it out myself to show it to him a couple of hours before. And for gosh sake, if it had that huge dent, why in the world would you install it?!?!?). I wanted to cry and told him to take it down. DH said he would exchange it and I told him to just return it and not get another. Not just because of the dent, but because I lost all that beautiful tile and the kitchen looked dark. It's just a simple white subway design, but it and the floor tiles are probably my favorite things about my new kitchen. Of course, now I have four small holes in the tile that have been filled with something white and I will have to figure out a way to camouflage them. I have a couple of ideas, but I'm not rushing into anything.

If one is grilling or frying, even a great hood will not stop splatters. Stainless will be very easy to clean. It's not dated - I see it all the time in very high end kitchens, often with a stainless shelf as well.

I've never had a stainless backsplash, only a stainless cooktop. Based on that cleanup experience I wouldn't care for a stainless backsplash by my cooktop. Here's my backsplash.

North Oaks Kitchen Remodel by Sawhill Custom Kitchens & Design · More Info

I much prefer the stainless back guard. Who says it's dated, and who cares?

It's functional with or without shelf, that's personal preference...

Although we did tile, I did consider a stainless steel backsplash with shelf. I love that look. I think it's very classic for any style.

Another option - we pulled our cooktop and counters out 10" or so; have a stainless steel surround around the cooktop and tile backsplash. 4 years into this - no issues with grease on the tile backsplash. Love the functionality of SS! (Edited to add that we have a large sump and good hood).

3katz4me - love your lighting behind your hood, and shelf above the hood, and contrasts -rich, warm, welcoming look.