If you choose the option "jest", you have to decline the word "zwierzę", so it would be: Ryba jest zwierzęciem (instrumental case). If you choose the option "to", you have to use nominative. Consequently, the sentence "Ryba jest zwierzę" is incorrect. You can choose both options.
The word 'to' generally means 'this' and is used for neuter nouns (to dziecko - this child, to zwierzę - this animal, to badanie - this research).
'To' is also used in two grammatical, easy construction, which you experience in the first lessons.
'To jest X...'; X being in nominative case, translated as "It is X" ie. To jest chłopiec - It's a boy; To jest dziewczynka - It's a girl.
'X to Y'; both X and Y being in nominative case, translated as "X is Y".
Hope it helps exploring the mysteries of Polish :D
Which part? If you get a Polish sentence to translate, you have to translate it as a correct English sentence. "Fish is animal", "The fish is animal" and similar are not correct sentences.
If you translate just one word/phrase, then you can treat it as in the dictionary, so you don't have to write "an animal" nor "the animal", "animal" should be ok.
"zwierzę" is Nominative, the basic form of the noun. It's mostly used for the subject of the sentence, but also in a sentence like here, "Ryba to zwierzę".
"zwierzęciem" is Instrumental. It's mostly used after the preposition "z" = "with", and it is also a valid alternative translation here: "Ryba jest zwierzęciem".