What types of Whole Wheat Bread should she buy, to imitate "grilled bread"? She worries that not all grillable breads can be seared on the stove.
Any kind of bread can be toasted/grilled. The only things you really have to worry about are whether it has a flat surface to evenly cook and whether it's so crumbly it'll just fall apart. Anything you buy sliced will work, and anything you can cleanly slice will work.
Note that an electric stove is not the easiest way to toast bread, since it isn't designed to radiate heat. The easiest method is probably to butter the bread then put it butter side down in a pan, so the recipe you linked is fine, but plain bread is a bit iffy.