Here are my choices:
Deluxe: Asiatic Lion
Seems only fair to get two lions when we also have two tigers: ideally, I would have liked to see the Southern Lion in the base game rather than the West African Lion; and also the Sumatran Tiger instead of the Bengal Tiger. A third tiger through the deluxe edition would have been too much in my opinion.
Arctic: Musk Ox
The Arctic Fox would have seemed an ideal addition, but since we received them in the North America Pack, I'll go for Musk Ox in this one, because it seems like the Arctic species we might not get a chance to receive anymore in any other pack.
South America: Maned Wolf
With the inclusion of the Capybara in the Wetlands Animal Pack, the Maned Wolf seems like a great inclusion to supplement the SA grassland roster (plus to allow for mixed exhibits with Giant Anteaters). A coati also would have been cool, but it seems like Frontier wasn't quite there yet with smaller models at that point of time.
Australia: Emu
Many sensible choices here, e.g., wombat, echidna, perentie. But the Emu is perhaps the most needed species for Australian exhibits, as they are present in zoos around the world and work wonderfully for shared habitats with kangaroos. I also would love a smaller wallaby species, but getting more than one kangaroo in one pack seems unlikely. Tasmanian Devils are also highly requested, but I think they would be great headliners in their own right, and if we hope to see Frontier support the game for many more years, we still need some high-profile inclusions for the future.
Aquatic: Australian Pelican
Would give us some much-needed Oceania representation, plus another bird, plus our first pelican. Really would have gone a long way to add more diversity to the Aquatic pack.
Southeast Asia: Painted Stork
The Asian Small-Clawed Otter would have been a really great addition here, but without these guys, and leaving gibbons as headliners for a later pack, I would really like either a bird or a smaller animal. We also have several small carnivores in the pack already, so I would skip the Yellow-Throated Marten with heartbreak to include the Painted Stork instead as our first stork and another bird to complement the roster.
Africa: Addax
As much as I would have loved another primate in this pack (preferably the Gelada), I think a rare and beautiful antelope from North Africa might be the best choice here, so I'd add the Addax to that pack.
North America: American Black Bear
I was already really happy with the animal selection of this pack, so I struggle to think of what else to include here. Peccaries or raccoons would be cool, but lately I have started to think that I'd love to have the American Black Bear for NA sections in my zoos, so even if it's essentially a "clone", that's my choice here.
Europe: Wisent/European Bison
Several possibilities to consider here, including Red Fox and Wild Boar, as animals that I would love to also see in the game at some point, but since I love my ungulates, I'm going for what's essentially another "unpopular reskin" and include the Wisent here.
Wetlands: Shoebill
Not really a stork, but rather a stork-like bird; and this would make for a fantastic addition to this pack, particularly next to the crane. In my line-up we already received the pelican, otherwise that would have been my choice here.
Other great additions would have been Fishing Cat or Allen's Swamp Monkey.
Edit: fixed stupid typo in first paragraph