A lot of folks like to do a tile backsplash that runs to the top of the countertop. If you plan on doing a granite or quartz countertop. I would consider doing at least a 3 to 4 inch backsplash of the same granite or quartz countertop material. Granite or quartz offers better water protection around the kitchen sink area than a tile grouted application. When removing old kitchens I have seen the tile and/or grout failing in that area most often.
I nice look is to bring the granite or quartz backsplash up to the bottom of the window sill at the sink area... Unless of coarse you don't have a window at the sink area. Then I would plan on a 4 inch high by 3/4 inch thick granite or quartz backsplash that would sit on top of the countertop. The installer will then put a generous amount of clear sealer between the bottom of the backsplash and top of countertop. Then it would make it really easy to clean at the back of the sink.
After the 4 inch backsplash goes in... You can still add the grouted tile later.
Next time I am measuring an old kitchen, I will take a few photos of where the grout is starting to fail around the sink area.