Stabilizers break down to four different categories: Cut Away, Tear Away, Wash Away and Specialty. Now it varies per company what they consider "Specialty" vs one of the other categories but no matter what ya call em, I think you should have these three stabilizers/interfacings in your sewing room.
Softweb is my favorite paper backed fusible web. Soft web is used for applique projects like my Limone Block. I love Softweb because it's clear, it's thin and keeps your project nice and soft (not bulky) so it's great for quilts.
In my blog post about 12wt thread appliques I compared Applique Fuse and Fix (which I also love!) with Soft Web, both are great but you will use them for different types of projects. Heat N Bond lite will do a good job in a pinch but over all I'm always much happier with my Soft Web results.
How I use it: I fuse it to all my appliqued fabrics, that's whether I am doing machine applique or machine embroidery applique.
OESD Fusible Fleece
OESD's Fusible Fleece is my favorite fusible fleece on the market. Like all OESD Stabilizers Fusible Fleece comes on a roll and can be bought in 10", 15" or 20" rolls. I love OESD's Fusible Fleece so much because of how easily it fuses to fabrics and because I like that it's lightweight.
Since it's on the thin side, if you're looking for something thicker you can try another brand or do as I do and double layer it. I'm rarely happy with other brand fusible fleeces, so I just layer this one as necessary.
How I use it: I like to use it as a stabilizer in my embroidery projects to create some loft and allow my stitches to sink into the fabric in a pretty way. I especially like it for embroidered pillows and table runners.
And of course, I use it in any project that calls for fusible fleece.
OESD Fusible Woven
Now, OESD actually calls fusible woven a "cut away" stabilizer, not a "specialty" stabilizer but they are the only brand to that sooooo...I'm putting it here! There are lots of woven fusible stabilizers on the market but fusible woven is my over all favorite due to the body it gives the fabric, the availability of the products,
I do like Dream Weave/Dream Weave Ultra from Floriani but it can be hard to find, when I can find a bolt of it I buy that. Typically though, I just buy a bazillion rolls of Fusible Woven at a time.
How I use it: I use it on freaking every woven fabric that I ever embroider. You will hear me sing it's praises in soooooo many posts and lives. I LOVE fusible woven and I think ya need to get it immediately to make all your projects go perfect.