The First Amendment is, in my opinion, the most important (which is probably why it was put first). I have heard the right to freedom of speech called "the guardian of every other right" and this is why I think that the First Amendment is the most important.
If we had all sorts of other rights, but no freedom of speech and press, our other rights would be worthless. If someone infringed on your rights, what could you do? You couldn't speak out against the infringement. You couldn't write an editorial criticizing the government for taking away that right.
But with the freedom of speech, we have the right to kick up a fuss when our other rights are violated. This is why I think the First Amendment is most important.