Always save your graphic files at the lowest bit depth adequate to the effect you seek. The traditional techniques of duotone and tritone can also be effective on Web pages and they typically require modest bit depth. This is normally most useful for removing the backgrounds from drawn objects or type, which then appear to float on the browser window background color along with the standard fonts and other elements. Such floating images are often preferable to an arbitrary welter of rectangles with no considered relationship to each other or to the shape of the browser window. Anti-aliasing softens jaggies by blending intermediate tones between object color and background color at the edge of the object.
Transparency can only replace one shade, however.
If the GIF has a background much different from that where it will ultimately appear, making the background transparent will still leave a halo effect around the object after anti-aliasing. Other things being equal, a good choice for a default background color to define as transparent is Mosaic standard gray. Don't forget to provide informative alternative text for your graphics. Text-only browsers like Lynx, and graphical browsers configured not to display images, will not show graphics files. HTML therefore provides tags for alternative text.