Aurifil's 80wt cotton is the finest cotton thread I've found. Because it is a fine thread, you may find it better to work with shorter lengths of thread to cut down on fraying and knotting as you work. I use Thread Tamer to condition the thread.
This is the best thread I've found for hand appliquéing fine cotton fabrics, like cotton lawns. In this set of six spools you'll find thread colors 2710, 2740, 2520, 2423, 2410, and 2021.
You can use this thread to hand appliqué regular cotton fabrics if your stitch length is short, 1/16" or a little bigger. If your stitch length is closer to 1/8", this thread is probably not your best choice.
This fine thread is dandy for English paper piecing, where there are so many stitches, packed closely together.
You can use this 80wt cotton in some machine sewing. I love this thread for straight-stitch or blanket stitch machine applique. In my machine, I don't usually have to adjust the tension. I use the same thread top and bobbin.
I haven't tried it, but this thread could also be good for machine embroidery.