I have pieced backing fabrics both ways. If the fabric is directional, it is seamed vertically. I use a half-inch seam allowance and then press to one side. That is finished with a line of top stitching which helps hold that seam. Plus lots of starch along the seam line.
I make sure to match the direction of selvages when piecing. If the selvage is on the LEFT of piece number 1 it is also on the LEFT of piece number 2. Selvages are trimmed off the backing. I also stay stitch around the backing.
Backing is starched, ironed and folded on a hanger for the quilter. It is also marked TOP and BOTTOM and shown to the quilter at the consultation.