My advice for scanning a signature:
Use a Calligraphy Pen, something with a decent width to it. It makes the selections in PS easier if it has more pixels to work with.
Scan it at the highest resolution possible
Use a very clean piece of paper, preferably gloss. You will have less marks/dust etc to clean up and confuse a quick selection.
do 2 final versions.
One with a white background, and one with a black background. That way you can apply a white signature on a dark background and a black signature on a light background using layers and blend modes.
Saving as PNG allows you to completely remove the background (neither white nor black) JPEG does not!
A cheats way of doing the selection:
Menu: Select > Colour Range
Set it to shadows and it should automatically select all of the text (as well as any dust marks)
Deselect any dust marks, and use the background eraser tool - Right click the eraser tool - to remove the background completely. Be thorough, any dust marks will show up.