This does not create a transparency, it will remove the selected area and replace it with the currently Background Color - white by default. If your web page uses solid white as a background color it will have the appearance of having transparency, but in effect it is blending in.
If you have a solid color other than white as your page background color then you can use the same steps after changing the Background Color in Paint to match. If that is what you have then this answer is more than sufficient.
If your pages have a polychromatic or image background then images with white (or other single color) regions substituting as transparent will stand out.
Since this is not creating a transparency, but rather editing the image, save the image in a format of your choice that will retain the quality of the image. (It does not have to be GIF since this format most often reduces the quality of the image if it was originally something better, such as anything 24-bit.)