if it's for web purpose, try to save it as a transparency GIF format but make sure your image (the one with the drop shadow) layer is etch out and not flatten with the white background.
some later version of browser such as Mozilla's Firebird will have the ability to read PNG files which is a better file to show transparency..
To crop your image, no matter how tight you crop it, you will still see a very thin white line around your image if it's pasted on a coloured or texture background. the best way is to do your editing in the background colour that it's suppost to go to.. that way, it will not have any problem.
hope it helps