The back will mirror the front. For Example, if your design is a basket of flowers, quilting around will produce an outline, sort of like a shadow. If you quilt around, then echo the flowers, it will look more like a basket of flowers again. Putting a grid through it would produce an even, but boring back, and not do justice to the front.
And then there's always trapunto, if you really want to add dimension.
So tell us more about dear Hannah.