You can get a favicon Photoshop export plugin here. (you want the .ico format, and your icon needs to be 16x16)
For ideas? There aren't all that many many "generic" symbols that get weather across in that much space :/ If you have an easily spotted color scheme or name (initials in that much space) or the like, that might be another path to take. For bookmark lists etc., it's probably more important that the users can quickly spot it as your site than a weather site, since they probably put the bookmark there and know what the content is.
I've heard that you can save a 16X16 or 32X32 BMP image then change the file extention to .ICO does this work or will I have to go with the Icon plugin?
I'm lazy I can't be bothered installing crap if I don't have to.
ico is a container format, much like Mac icns. The images inside an ico container are nearly identical to standalone bmp images, so you may get away with renaming, if we presume that all the browsers out there are sufficiently lenient.