As someone who mainly builds zoos based in Australia, the first and foremost choice for me has got to be the Australia Pack. This is the only DLC we've ever gotten where every single species included is kept in Australian zoos (as expected), and not only that, each is very commonly kept and arguably essential for building a zoo here. Combine this with some fantastic and essential foliage (such as the game's only Australian eucalypts) as well as great scenery pieces (all that metal mmmm) and it easily tops the list as the most essential pack for me.
Next up comes the Africa Pack, which is just a fantastic pack all around. The meerkat, fennec fox and southern white rhinoceros are all great and essential species that I include in the majority of my zoos, but I also really love the foliage in this pack as someone who's a big fan of deserts, scrublands and xeric environments in general. The new plaster pieces that come with this pack are very useful and versatile, but the wood pieces arguably steal the show for me - they're my default choice when it comes to creating structural supports on buildings and such.
Third would of course have to be the Grasslands Animal Pack, which seems to follow the trend of the obvious three packs here all being themed around drier biomes. The species selection in this pack is just so strong, with the wallaby, emu, maned wolf and caracal all being particularly important to the kind of zoos I build. Plus, those butterflies!
The fourth pack here was actually surprisingly hard to choose, with me considering the Southeast Asia Animal Pack for a while, but in the end I went for what is also my fourth favourite DLC, the Wetlands Animal Pack. The capybara, platypus, Asian small-clawed otter and water buffalo are the standouts from this pack for me, but I also just like its whole vibe. Shame it comes with no music though!
Tragically this list does not encompass my favourite animal in the game, the common wombat, but the rest of the Twilight Pack wasn't strong enough for me to place it over any of the other packs in this list (although the bats are also a huge draw).