There is no simple answer, the answer depends on the image contents and on the number of unique colors in the image.
For photos jpeg is the best option, compression is lossy, but for the human eye the differences are not that dramatic. You can adjust the compression level (some tools allow it, some not).
For small images, with a maximum of 256 colors .gif or .png are good. Both use loss-less compression.
You can use an image converter to test some of the possibilities (gif, png or jpeg).
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