This is a very personal question due to how it emphasizes an individual reader's experience. Feel free to pick whatever 2 quotes had a more significant impact on you. If that prompt is too wide open, then I recommend picking quotes that highlight either the characteristics of a person in the story or a theme. This will narrow down the field of quotes for you to comb through.
The theme of good vs evil is present throughout the novel, and it is a theme that Tolkien will really develop in the later trilogy. Many characters are good and many are evil, and I believe that most readers would agree that Bilbo is representative of good and Gollum is representative of evil (or being corrupted by evil). A really good quote showing these character traits and this theme comes in chapter 5.
[Bilbo] must stab the foul thing, put its eyes out, kill it. [Gollum] meant to kill him. No, not a fair fight. He was invisible now. Gollum had no sword. Gollum had not actually threatened to kill him, or tried to yet. And he was miserable, alone, lost. A sudden understanding, a pity mixed with horror, welled up in Bilbo's heart: a glimpse of endless unmarked days without light or hope of betterment, hard stone, cold fish, sneaking and whispering.
Bilbo can't fathom killing an unaware and unarmed enemy. The idea of an unfair fight appalls Bilbo even though it would help save his own life.
Chapter 18 has another good quote that shows just how deeply set Bilbo's moral code is. Bilbo intimately knows what is good, right, and true, and that knowledge forces him to make sure that his relationships are set right. This means giving payment for goods received or services rendered. Bilbo is not a person to take advantage of anything or anyone. He truly is a good person (hobbit) that stands against even the simplest of evils.
"I beg of you," said Bilbo stammering and standing on one foot, "to accept this gift!" and he brought out a necklace of silver and pearls that Dain had given him at their parting.
"In what way have I earned such a gift, O hobbit?" said the king.
"Well, er, I thought, don't you know," said Bilbo rather confused, "that, er, some little return should be made for your, er, hospitality. I mean even a burglar has his feelings. I have drunk much of your wine and eaten much of your bread."
"I will take your gift, O Bilbo the Magnificent," said the king gravely.