I kinda recommend playing the Story first, actually. As a PSO fan, I got PSU the day it came out and rushed online but...
...when I just got back into it (on the Xbox 360 version) I decided to play the Story before going online,
and I enjoyed it a lot more.
And you still get Extra Mode offline--you can create your own character and wander the universe and whatnot,
it's just not as fun without your friends.
