Making sense of archiving and lossless compression?

For everyday files and folders, there are many data compression and archive formats, such as zip, gz, 7z, bzip2, and such, and there are many algorithms, such as DEFLATE, LZMA, LZX, etc. If you have all these choices, are there guidelines for which one you should use, depending on what you are doing? Are there certain circumstances under one of them is the best one to use, and are their certain circumstances where some are bad?

This is really confusing me, and I've looked everywhere, and can't find an answer. Perhaps someone could shed some light on this.

Update:

I'm not wondering the best software, I'm wondering the best algorithm under certain situations.

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