As someone who just spent a week in the New York Metro area last month and visited all of the WCS facilities, I have some advice I can offer.
First off, I compiled a species list from my trio of visits last month which you can view here ->
[VISIT] Bronx Zoo Species List - 2024/06/16. I wasn't initially planning on sharing this until I got to my review, but that's going to be a while.
How many days and how much time per day are you planning on allocating? The Bronx Zoo is indeed huge, and even if you just prioritize mammals, that would still require you to visit almost every corner of the zoo to see them all (you're looking at about 100 species to see). For mammals, and especially rare mammals, I would prioritize the following exhibits: Madagascar, Congo Gorilla Forest, Wild Asia Monorail, Jungleworld, African Plains, Gelada Reserve, Mouse House, Tiger Mountain (can skip if you don't need to see tigers, but Pere David's Deer are nearby), Himalayan Highlands (can skip if also doing Central Park), Bears/Dholes, and Bison Range (can skip if also doing Queens).
Also. how are you traveling to the zoo? Regardless of how, I would plan to arrive early, maybe before opening, and getting in at rope drop so you have the maximum amount of time to see everything (as this is your first time, you don't want to rush it). The Bronx Zoo has really short operating hours for a zoo of its size, and they close
all animal exhibits 30 minutes prior to the listed closing time (so for example, they are open 10am-5:30pm on the weekends, but the exhibits are only open until 5pm).
Regarding the other NY zoos you mentioned; if you are only visiting one other zoo and are still prioritizing mammals; Queens has the coyotes (although they were no-shows on my visit) and Andean Bears as well as Elk; Prospect Park has the 2nd highest mammal species count in the WCS, but there is some overlap with Bronx, but they still have species like Black-footed Cat, Pallas Cat, Straw-colored Fruit Bats, North American River Otter, and Sand Cat. Central Park has Japanese Macaques, Banded Mongooses, and Black-and-white Ruffed Lemurs (I have species lists for this places as well if you are interested).
And lastly, all of the WCS facilities require you to reserve your timed ticket online in advance, so make sure you check the website. The Bronx is unique in that they have several attractions that would normally require an extra fee, but you can easily purchase a full ticket that grants access to all of these attractions.
The zoo does not have American Beaver, Nine-banded Armadillo, or Yellow-bellied Marmot on exhibit anywhere in the zoo (unless they have them as ambassador/program animals, which I am no aware of). Wild beavers do inhabit the Bronx river, though. The rest are present.
The Bison Range does not require an additional fee. In fact, the tree kangaroo is the only one on the list that is held in a star attraction.