You may as well get the black & white 1968 classic Night of the Living Dead, by George A. Romero. It's a true zombie movie (I wouldn't classify 28 Days Later as one), and influenced pretty much every horror and zombie movie that came after it, including Shaun of the Dead. It more or less defined the rules of the zombie genre.

It doesn't really hold up to what we have today: The acting isn't noteworthy and the special effects are what you'd expect from 1968, but that's what you'd expect from a pioneer film, I guess.