JPG is lossy, which means it takes out parts of the picture while compressing it. You'll get the smallest size with JPG, but the worst quality.
GIF is also lossy, but it's less noticeable.
PNG is the best overall format you can use, you never notice any loss from compression and it's very small
I've made some examples for you, this contains a TIFF file, and GIF, JPG, and PNG images converted from it with various levels of compression: [Link](Mouse over link to see full location)
(the ads on that page might be a bit NSFW, sorry about that)
The best thing to do is use JPG with medium compression for all of your real-life pictures. Use PNG for everything else. You can convert images with irfanview: [Link](Mouse over link to see full location)
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