English statement:
Somebody in your class is a zombie.
Assuming the domain of $x$ is all people, should this be:
$$\exists x ( C(x) \land Z(x))$$
or
$$\exists x (C(x) \rightarrow Z(x))$$
My guess would be the first one, but when the sentence changes to
All people in your class are zombies.
My guess changes to
$$\forall x (C(x) \rightarrow Z(x))$$
Are my choices correct?
Yes, your first existential choice is correct (as is your universal choice).
The other existential choice, "$\exists x (C(x) \to Z(x))$", is equivalent to the statement "there exists someone who is either not in your class or is a zombie", which would be true, for example, as long as there existed someone somewhere who is not in your class (even if none of your actual classmates were zombies).