I haven't read the books, I have read up on each character's story a bit here and there though without trying to spoil the show for myself, lol. But what really did it for me was, about a week ago I was bored and went back and watched all of season 1 and season 2, and it really made me understand things a lot better and pick up on ton's of things I had previously missed.
The thing with Syrio and Jagar is something that is up for debate by people who have read the books. So far the books haven't confirmed Jagar is Syrio, but of course two books still remain to be released. So it could wind up being so. But the show definitely seems to be trying to point the viewers in that direction.
Now, one thing I did accidently read up on was the future of Robb and Theon. Especially one particular part all the book readers are waiting for, The Red Wedding. I don't want to spoil things, so I won't say anything. But there should be some kind of pick up around the events of what happened at Winterfell in the beginning of season 3. Well, that's if they go the direction of the books. But what happened there in the end of season 2 will set the stage for Robb and Theon's future.