Some people might argue that a truly handmade quilt can't be made with the help of a sewing machine. However, a machine can give you advantages in speed and consistency. Besides, if you do use the machine piecing quilt technique, it's still you running the machine.
If you opt to patchwork your quilt by machine, set the sewing machine's stitch length to 10 to 12 stitches per inch (or between 2 and 3 on machines that do not use the stitches per inch measure). Stitch across the seam allowance, along the seam line, and across the seam allowance at the far end of the seam. Do not backstitch.
Make sure the seam allowance is consistently 1/4 inch. The presser foot on a few sewing machines is a true 1/4 inch. Stitch a sample and measure the seam allowance. If you are off by just a hair on each piece you stitch, the errors will accumulate, and the end result may be distorted.
If your sewing machine does not have a mark or a 1/4-inch-wide presser foot, place several layers of masking tape to act as a sewing guide. Make a sample and measure it for accuracy.