I use YLI brand invisible thread, which is very fine -- similar to a strand of hair. It may not be available locally, though. I think there is a polyester invisible thread widely available in JoAnn's, etc., that people like. If you have a chance to check, you want a thread that is very flexible, not wiry or thick like fishing line.
Whichever invisible thread you use, loosen you top tension. This type of thread has a tendency to stretch; that's why it's better to loosen the upper tension. You shouldn't need to adjust your bobbin tension.