I pondered this question in a blog post several years ago. Revisiting it today, the solution seems pretty simple to me. Metallica made 10 studio albums so far. I can just pick the most popular song from each album for this list. If you listen to these 10 songs in order, you get a nice chronological progression of Metallica through their career.

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1. Seek & Destroy
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from the album Kill 'Em All (1983)