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  to condition the thread.

This is the best thread I've found for hand appliqueing fine cotton fabrics, like cotton lawns.
You can use this thread to hand applique 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  or  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.