I don't use stabilizer in my hoop when I'm doing quilting designs. The quilt sandwich is plenty stable enough. I use an air erasable marker to make a cross hatch in the center of my block, then hoop my quilt sandwich, lining up the cross hair marking with the center marks on my hoop.
Getting a quilt sandwich in the hoop can be a pain for some machines hoops, some machines have a quilting hoop.
Cari