Best: PNG 8 bit Indexed (essentially gif format but with compression in both vertical and horizontal planes)
JPEGs massively depend on the choice of colours as to whether they are better or worse than 8 bit GIF (Almost always smaller but sometime horribly messed up with artifacts).
Also, when my PC is working again, poke me for event banners as I have all the tools and do that kind of thing on a daily basis.