Invisible thread for quilting should not feel like fishing line. It has more of the qualities of fine hair. In the past, I have used YLI. I forget the specific dimensions of this thread, but it is very fine. Nowadays experts like Susan Schamber seem to prefer polyester threads such as Sulky. I'm planning to try that next.
It's fine to use fine invisible thread on top and a cotton thread on the bottom. With the YLI invisible thread I used, it was important to loosen upper tension on the machine. This is because YLI stretches a lot more than cotton. I would expect the same is through of Sulky polyester, but I'm not sure. Basically, what you want is that the invisible thread is pulled through to the bottom so you have "dots" of invisible thread on the bottom. Loosening the upper tension creates this scenario. You do not want "dots" of cotton thread showing on the top of your quilt.
Mary