Couldn't we just add an alpha channel, then go "Color to Alpha" and convert the white to transparency? This could have been done as "step" 3, without the use of the "Select by Color" tool. Then save as a png image.
Also we can skip the "save by file type" option if we know what file type we're saving in. Just type ".png" (without quotation marks) at the end of the files name and press "Enter".