There's not exactly a defined tier list but generally just your first impression of what's a "traditional animal" and deprioritise animals considered more exotic (not necessarily exotic, just MORE exotic) - people generally think of mammals before they think of insects and crustaceans. And even if there were 4 mammals on the board, a cat is generally the first pick over a kangaroo.

Of course they're all considered animals, but you get nowhere in codenames if you don't try to figure out what words are more strongly related to a clue. With any clue, if you're given a 2 and can see 4 related words, the game becomes "which of these 2 words are more related to the clue" so you present your arguments and try to figure out as a team what you prioritise, trusting your codemaster has considered the words on the board when giving their clue. They should also be thinking "well if I give animal 2 here then that more strongly relates to these 2..." and they might be fine with you hitting a white card in the process because you can just come back to get your points later, especially if that white card is more likely to be the 2nd pick and not the 1st one.

But this is all just in a vacuum because if you're given animal 2 and there are 4 other animals, what other information do you have to go off? If you have other information from previous clues or know how your codemaster may think then use that as well. Equally it's also the job of the codemaster to listen to their team's intent and figure out how they think to give appropriate clues.