For a more palatable chapter of the .hack 
series, I would suggest the Tasogare no Udewa 
Densetsu (Legend of the Twilight Bracelet) 
series.  It's much more straightforward, fun, 
cheerful, and action-oriented than the 
main .hack story (which is still be ironed 
out).  All you would need to know is that 
Tasogare takes place 4 years after the events of 
the first series (and the game).

Hey, when pretty much everyone is in Super-
Deformed mode and the theme song is performed by 
Round Table (famous for Chobits OP), Tasogare 
can't be that bad, right?