I would use my serpentine stitch and stitch from the top to bottom starting in the middle and stitch to the right edge. I would then flip the quilt and start in the center again to do the other side. As for quilting horizontal lines, you don't have to do them and as each line crosses the vertical lines you have a potential for creases at the intersection in the backing. If this is your first quilting try, I would stick to just verticle lines.