from an instructional standpoint, what do you believe to be the four of the most important quotes in Fahrenheit 451? Excerpt and record each. Support each quote with reasons why it is noteworthy.

Different teachers are probably going to choose a slightly different set of 4 quotes depending on that teacher's personal reaction toward the book or personal teaching strengths.  
I think Beatty has some great quotes, but I'll limit him to one quote.  The following quote is from part 2 of the book.  

"What traitors books can be! You think they’re backing you up, and then they turn on you. Others can use them, too, and there you are, lost in the middle of the moor, in a great welter of nouns and verbs and adjectives."

The quote is important because Beatty's quote points out exactly why books and literature are awesome. They force readers to think. 
Montag has a lot of great quotes that could easily be used in the classroom. The following quote is from part 1, and it is eerily similar to Beatty's quote.  

"You weren't there, you didn't see," he said. "There must be something in books, things we can't imagine, to make a woman stay in a burning house; there must be something there. You don't stay for nothing."

Beatty thinks that books are all nonsense because they don't expressly tell you what an answer is. The woman from Montag's quote is the opposite of Beatty.  She doesn't see the books and their questions as nonsense. She sees them as worth dying for.  
As a literature teacher, I really like the following quote of Montag from part 2. 

"Nobody listens any more. I can't talk to the walls because they're yelling at me. I can't talk to my wife; she listens to the walls. I just want someone to hear what I have to say. And maybe if I talk long enough, it'll make sense. And I want you to teach me to understand what I read."

I like this quote for two reasons. The first is that it points out a basic desire of humans. We are social. Montag longs to be in conversation with people about his thoughts, ideas, and dreams; however, neither the television nor his wife are capable of giving him an intellectual relationship. The second reason I like this quote is that is points out a basic need for teachers and experts. Montag may know how to read, but he isn't sure how to interpret what he is reading. He needs a teacher to help him better learn. It shows that teaching and learning is best done in a community setting.  
The final quote occurs during a conversation/argument between Montag and his wife.  

"Let me alone," said Mildred. "I didn't do anything." "Let you alone! That's all very well, but how can I leave myself alone? We need not to be let alone. We need to be really bothered once in a while. How long is it since you were really bothered? About something important, about something real?"

The quote is a great quote to use in class because it points out that in order to really know that a person is happy, that person needs to experience sadness. You can't have the highs if you don't know what the lows feel like. Mildred doesn't get this. She is like many other characters in the novel. Their attempt to never feel sadness or be bothered by things prevents them from ever really being happy as well.