GIF or JPG? Truly an eternal question... with a relatively easy answer.
Understand that GIF and JPG are types of image compression. That is, the information contained in the image is compressed and condensed so it travels quickly over the Internet. Uncompressed images (such as .bmp files) are, relatively speaking, very large (in KB) and can take a long time to download. They are not very suitable for use in web pages.
GIF compression and JPG compression both reduce file size, but do so in different ways. With both methods, filesizes are reduced dramatically so that your images, and subsequently your web pages, load quickly. It's a common misconception that to convert a BMP to a GIF or JPG, all you need to do is change the file extension. That couldn't be more wrong. What you need to do is load that fat BMP into an image editor, and save it as a GIF or save it as a JPG. Most image editors have controls for varying the degree of compression. With a little practice you'll be an expert... I promise :-)
Ok Joe, you're starting to bore me... should I save as a GIF or as a JPG??
Like I said, it all depends on the type of image. Photographs or images with a lot of gradients or changing colors are more suited to JPG compression...
Drawn images with relatively few colors are more suited to GIF compression...
You may also find interesting GIF Compression Explained and Image Compression Examples.