Show that every countable, first countable, zero-dimensional T1 space $X$ is metrizable.
I know that T1 space means that all its singletons are closed. Also, zero-dimensional means that $X$ has a basis formed by all the clopen sets.
Moreover, I know that if I prove that the space is regular with a countable basis, then that implies it's normal, and if it's normal and second countable, then that implies metrizable.
I feel like I'm making this too complicated, and I'm not sure where to start.