Neat quilting can be achieved if the quilt top and backing are straight to begin with. Always cut the fabric on the straight grain to ensure a straight edge.
Fullness and puckers pieced into the quilt top cannot necessarily be quilted out. I will only do my best, but quilt tops with these problems may still have the problems after quilting is completed.
Backing and wadding should be cut on straight grain and 3-4" larger than the quilt top on each of the four edges.
Do not baste or pin your quilt together.