Ubuntu Desktop or Server ISO on USB key
Solution 1:
As you write in the question, you can start from both a desktop iso file and a server iso file.
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I think it would be easier to make it work from a desktop iso file, because it is easier to make a portable system that way, for example as a persistent live system made by mkusb-dus.
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If it is important to make a light-weight system, you should start from a server iso file. The server must be installed into the USB drive, and if you want a portable network, it must be fixed.