Do you always use a blanket stitch to applique? Not always, but usually. Sometimes I'll just fuse it on & use a running stitch.
What about hand stitching vs. machine stitching? I personally prefer hand stitching, but I've seen people who've done it by machine with 12wt thread.
If hand stitching, do you use thread or floss or does it really matter? I've used Aurifloss, perle cotton & 2 strands of embroidery floss. They all work. The reason for using something thicker is due to the stitch length/spacing. When working with felted wool, you have a longer stitch length because the thread is traveling the height of the felt in addition to whatever horizontal spacing between your stitches. I usually will do 1/4" for both the length of the stitch & the width between stitches (generally they should be the same with a blanket stitch). That's a stitch length of over 6mm, so I want something that is at least a 12wt cotton (or a wool/cotton blend like Aurifil's Lana). If you were somehow doing a shorter stitch, you could maybe try a thinner poly thread, but I'm not sure why you would want to. If you don't want it to show, pick a matching color of thread. A thin thread looks a bit strange to me on the edges of felt. It's hard to get it to lay nicely & it also leaves much of the edge exposed, with just thin little bits of thread running across the edge. Unless that's done intentionally -- for artistic reasons -- it's rarely as nice of a finish as a heavier weight thread/floss.