I like the outsides of my quilts to be 100% cotton. The batting may be a different story. I haven't had any problems with the cotton battings and prefer to use those, but I like the ones that have a stabilizing scrim in them. The scrim is not made of cotton, so then the quilt is not technically 100% cotton. I'm also not opposed to using a non-cotton batting, but I prefer cotton, because it will shrink with the top and backing.
As for thread, I like Connecting Threads cotton thread. I bought a huge amount of it a long time ago, and I'm still using it. I haven't tried anything else in ages.
I don't really embellish my quilts except for a label, which I make out of a scraps of cotton quilting fabric and cotton embroidery thread.
I guess I'm a "cotton girl"
C