Ted Chiang is cool. But I think "Story of your life" isn't his best work. If you're going to read one story by Chiang, a good one is "Liking what you see": http://www.ibooksonline.com/88/Text/liking.html
Personally, I think Story of Your Life is a master work. I found the strange writing structure annoying at first, and then right at the end of the story you get an "ah-ha" moment that changes everything. What I thought was awkward writing turned out to be a masterful illustration about a theory of consciousness. I was floored by Chiang's ambition to even write such a story.
I saw Arrival last night, and was very struck by the fact that despite having read and loved Stories of Your Life and Others, I couldn't remember anything of the plot.