Quiltvillage and American Patchwork & Quilting magazine instructions list pieces in the order they should be cut to make the best use of your fabric. Always consider the fabric grain before cutting. The arrow on a pattern piece indicates which direction the fabric grain should run. One or more straight sides of the pattern piece should follow the fabric's lengthwise or crosswise grain. The lengthwise grain, parallel to the selvage (the tightly finished edge), has the least amount of stretch. (Do not use the selvage of a woven fabric in a quilt. When washed, it may shrink more than the rest of the fabric.) Crosswise grain, perpendicular to the selvage, has a little more give. The edge of any pattern piece that will be on the outside of a block or a quilt should always be cut on the lengthwise grain.
In projects larger than 42" in length or width, Quiltvillage and American Patchwork & Quilting specify that the border strips be cut the width (crosswise grain) of the fabric and pieced to use the least amount of fabric. If you'd prefer to cut the border strips on the lengthwise grain and not piece them, you'll need to refigure the yardage to accommodate this.