Yeah the general story in Saw I-III isn't overly played, but after the reveal of the new villain at the end of IV, they do become quite arc heavy for V-VII.
Basically in each Saw film there are two plots, one of the person playing the game with all the blood and guts, and the other of the arc plot.
With all the various characters and the interconnecting flashbacks throughout each film (a lot of the time expanding on scenes in other films) a newbie could watch and follow the horrific "game" story, but I think they'd be pretty lost by jumping into the arc plot.
You know, I really enjoyed PA3, so this isn't a major criticism. But after I saw the first two, I went to bed that night, turned off the lights... and my mind wandered to the movie I'd just seen. And damn it if I didn't want to turn the light on! And be getting nervous if I heard some random noise from downstairs.
In fact I remember after seeing the first one, I had to take a leak in the middle of the night, and our bathroom is downstairs. So I went down, still thinking of that damn movie. It was really dark, I did my business, and as I came out of the bathroom I heard some weird sound from the living room. Now I'm sure it was just a normal house noise, but man it scared me half to death.
I almost ran upstairs to go back to bed!
Anyway, with PA3 I didn't get that at all. It kinda seemed in this movie a lot of the scares were more about the suspense (awaiting what that moving fan-camera would show us next) than actual jumps. Thinking about it the demon/Toby didn't really do that much freaky shit in this one as in the other two.
Also a minor irritation- why didn't the (hot) babystitter tell them about what happened to her? It wasn't like they wouldn't believe her or think she was crazy, it was all there on the cameras. You think they might want to know "oh by the way your house is haunted." And that scene of her looking into Toby's cupboard "lair." I wonder what she saw?