Stabilizing the quilt: This is pretty straightforward for most quilts. If you are using a domestic or George-type machine, you will want to pin or baste the top, batting and backing together. A longarmer can do this for you quickly and at a very reasonable price.
Chemical/glue/fusible basting is problematic because you are putting some kind of chemical on the quilt, and these have a tendency to gum up your needles.
Like many longarmers, I float the quilt top, which means I attach the backing only to the machine, layer on the batting and top and baste those edges down. I quilt the area under the machine throat, advance the quilt, and baste again as I go. The only time I have had a problem doing it this way is with large medallion quilts, where the borders get increasingly smaller as you approach the center. I sometimes ended up with pleats on the backing of larger quilts.
To avoid this heartbreak, I took a tip from Sharon Schamber and baste a stitch line across the width of the quilt each time I advance it, before that section is quilted. Works like a charm every time, no matter how densely I quilt the sections!