There are so many stabilizers for you to choose from that it makes it hard to select the right one for the job.  Below are a few links to education sites and documents about keeping things stable. 

My favorite stabilizers are the following:
These can be purchased from many different companies.  
Cut Away - Whitefor sweatshirts
Cut Away Black for dark fabrics
No Show Fusible Mesh - this is great for t-shirts and quilting blocks
Tear Away Wash Away - another stabilizer good for quilting
Clear Wash Away - towels and anything needing a topper
Aqua Wash Away - the best for lace

Happy Stitching,