I have done both with and without stabilizer. My preference is without. It makes the stitching easier to do and provides and evener flow of movement when stitching. Like others have said a good spray starch or sizing is the best I know of to make things stay pressed while in the hoop.
I don't do a lot of hand embroidery anymore but when I do I have changed over to a nice linen instead of muslin I found it is much more stable to work with. Have fun with your embroidery!