Interesting question. I find myself periodically tweaking the available images on a taxon pages, and thus I have formed some personal opinions based on my usage of those images/pages. To your questions:
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Dynamic? FWIW, absolutely not! Stability in presenting optimal, identifiable examples of a species should be paramount. Certainly the best available images are likely to change over time, and those are fair game to add or trade out. The primary taxon photo, and any secondary ones available for quick examination on the taxon page should be there to aid identification and show variation. Nothing more.
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First images are only appropriate for the rarest taxa. As more and better images (for ID purposes) are available, the “first image” becomes irrelevant. There is a wonderful and informative project for “First Known Photographs of Living Specimens”–a great repository for those first taxon photos.
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Diversity? I think the array of photos accessible on that taxon page should include at least a representative array of expected forms (like sexual dimorphism or other pattern polymorphism), if available. The primary image should show a good view of the most common phenotype.
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Favorites or good in humbnails? Nope, absolutely irrelevant–unless a really good image of the typical form of a species is one of your favorites. A small number of times, I have traded out “artsy” images of a species for another image that shows what the plant/animal really looks like commonly. One caveat is that some well-cropped, high-res images, although excellent for examination in detail, may display an animal which gets “out-of-bounds” in the thumbnails on the taxon page. I view that as a minor annoyance because I normally want to click on the photo anyway to see a full-size view.