what are the most important quotes and why

I think that you must decide what is an important quote. I can give you a few to consider:

Love:

Love is a smoke raised with the fume of sighs;
Being purged, a fire sparkling in lovers' eyes;
Being vexed a sea nourish'd with loving tears:
What is it else? a madness most discreet,
A choking gall, and a preserving sweet. act 1

Romeo knows a little about the chaos and illogical passion of love.

Hate:

"What, drawn, and talk of peace? I hate the word,
As I hate hell, all Montagues, and thee.
Have at thee, coward!" act 1 sc 1

Tybalt hates peace: he would rather fight.

Fate:

What, drawn, and talk of peace? I hate the word,
As I hate hell, all Montagues, and thee.
Have at thee, coward! Act 5 sc 1

Romeo hllenges his fate after finding out that Juliet is dead.