I usually hoop the sticky stabilizer, stick the fabric on, then baste around it with the option available. I also add the water soluble on top before I sew.
One of the first things I embroidered was blues clues on fleece. Boy was that a learning experience. Talk about the outline being off!!
Sometimes I use the knit iron-on stabilizer and place it opposite to the grain of the fabric. It is not very heavy so it doesn't add too much to the thickness of the fabric.