Since she expressed an interest in Trek, it sounds like she already has a couple of episodes in mind -- otherwise it wouldn't have sparked her interest in begin with. Find out what those episodes are and watch them with her. Then find other good episodes from the same series she's interested in.
WWZ 2 will be interesting. I'm a huge fan of the book; and in my world, zombies shamble -- they don't run. Before I saw WWZ, I heard the only thing the movie had in common with the book was the title. So I watched the movie without prejudice -- to see how it would stand on its own. Aside how the zombies sprinted, the rest of the movie wasn't bad. WWZ 2 will be interesting.