There isn't a single answer for your question. There are many websites where you can learn all the reasons to use different type stabilizers. This is one
http://www.urbanthreads.com/tutorial...ing+Stabilizer
JoAnn Fabrics has a large selection of small packs of different stabilizers and each describe what their use is. Most stabilizers are based on embroidery, but the same rules apply for applique as embroidery. When I had to applique a Kool Kat cotton item onto a tee shirt, I used a medium weight tearaway to do it. The medium is harder to tearaway without breaking the stitches than the lightweight, but the lightweight would not have been strong enough to keep both fabrics stabilized.
Maybe someone with more experience than myself can give you some rules to go by.