The most invisible thread I have tried is YLI nylon monofilament (.003mm, about as fine as baby hair). Many people believe polyester thread will last longer than nylon thread, but I am not convinced. I have tried a couple of polyester invisible threads, including the one from Superior Threads, but they all show more than the YLI nylon monofilament. The Invisafil thread also shows more than YLI nylon. Actually, all of the invisible threads I have tried show more than the YLI nylon. I have never found good invisible thread locally; have always had to order it online.
There are some tips to using nylon monofilament correctly. It is a stretchy thread, so it is important to lower your upper tension several notches. You also want to fill bobbins slowly. For plastic bobbins, half full is plenty; for metal bobbins, 3/4ths full is usually fine. If you fill the bobbin fast, the thread will stretch and then spring back as you sew. if you overfill, the bobbin can distort.