(Now, with all that said: I've tried to read the books three times and I just couldn't do it. Wanted to. Couldn't.)
It's normal to be saying, 'What the **** is this?' when they're in Tom Bombadil's house. Just keep going - the hobbits are probably thinking the same thing. Also, read the Hobbit first, it's just as good.
My favourite moments all relate to scenes with any of Aragorn, Boromir, Theoden and Denethor. I feel that Tolkien wrote flawed leader/king characters very well and that Jackson interpreted them all very well.
To name a couple, I'd say Aragorn coming across his kin in the shape of the Argonath looked wonderful on film. Also I like Theoden's private reflection at the muster of Rohan 'So it is before the walls of Minas Tirith that the doom of our time will be decided,' he knows he's probably going to his and many of his people's deaths, but also knows the manner of their sacrifice will define who they are.