To help yourself remember quotes better, don't just recite them again and try to memorize them. Instead relate them to your personal life, the character's life from where they came from, or the context that it came from

This will help you understand on a deeper level and use them appropriately.
Very often the most memorable quotes are the ones that we all remember are the ones that we can deeply relate to our lives, where we can give it a personal meaning. That's what helped me remember a lot of the quotes deeply when I studied Year 12, as a lot of it related to my experiences. Here are a few example of my favourite quotes that even till today I still remember them (though not word by word, I needed to look them up) and how I they are deeply related to my life.
1) "Pursue some path, however narrow and crooked, in which you can walk with love and reverence." Henry David ThoreauGrowing up, we all have parents wanting us to have high paying stable lucrative jobs, and society wants us to fit in. I never liked the the idea of fitting in, and having a job just because it pays well, I'd rather do something that I'm really passionate about, even if the path is a lot more challenging and unconventional. This is why this quote resonates with me, because I want to walk a path I love, no matter how narrow and crooked it is.
2) "The mind is a dangerous weapon, even to the processor, if he not know how to use it discreetly." Micheal de MontaigneThe mind is a potentially a highly destructive to others and ourselves; you never know if a mean comment can shatter other's heart, and self beating thoughts can be very harmful to ourselves. This is why understanding the mind, and knowing how to use if carefully is important.
3) "Study hard what interests you the most in the most undisciplined, irreverent and original manner possible." Richard FeynmanI love this quote! Find something that interest you the most, and study it in your own unique way. I never liked having a too rigid study structure, but rather always going with the flow and letting my heart guide me
