Universal needles are not the best choice for quilting as they don't have a really sharp point-they are better for sewing with knit fabrics with the more ball point tip that they have...they tend to want to sew between the fabric instead of through the fabric weave so you don't get a really straight line of stitching.
I use the Sharps for piecing, usually a size 10.
For quilting I use the Quilting needles...size will depend on fabrics/batting/amount of piecing...they are very sharp and tapered and designed to go through the layers of fabric.
Before there were all the different needles that we have to choose from these days, I used a finer sized Jeans needle for piecing and quilting, so that is always an option too.
Happy quilting!