Important quotes in literature accompany important moments, the moments that reveal character, drive conflict, produce climax, support resolution. So what you are really asking is "What are some important moments in the novel?" The novel is structured in three sections: (1) Gilbert's frame introducing Helen Graham/Huntingdon; (2) Helen's diary of her marriage; (3) Helen's return to Grassdale Manor and Huntingdon and all that occurs thereafter. Each section will have pivotal quotations that mark them as important.
One moment that has importance in the first section is the seemingly innocent event of a visit to Helen's home. It is here that Gilbert accompanies Rose on a call to Helen and much is learned about her painting. She paints for profit, not amusement, as her paintings are sold in London. She signs false initials. It is also here that the plot is furthered because Gilbert and we learn that she ascribes a false location to hide both her location and identity (incidentally, a bold statement is made for someone in hiding and for someone else to gloss over as though unnoticed):
'I have friends ... from whom I desire my present abode to be concealed; and as they might see the picture, and might possibly recognise the style in spite of the false initials ...[I] give a false name to the place also ... if they should attempt to trace me out by it.’
In the second section, Helen's diary, the explanation of her disastrous marriage and its horrible effects upon the child is an important moment. One of the important quotes is the brief one that describes the child: "where [Arthur] was sitting half-tipsy, cocking his head and laughing at me, and execrating me with words he little knew the meaning of."
The third section presents us with the important resolution and the falling action leading up to it. An important quotation form this section involves the Christmas rose and Gilbert's, finally, successful suit for Helen's hand in marriage. Huntingdon has died and been buried. Helen's uncle has left her his estate where she lives with her aunt. Gilbert has sought her out under the mistaken news that she is being married to Hargrave. Gilbert and Helen establish that their feelings have not altered, and Helen says:
‘This rose is not so fragrant as a summer flower, but it has stood through hardships none of them could bear: ... the keen frost has not blighted it. Look, Gilbert, it is still fresh ... with the cold snow even now on its petals.--Will you have it?’
"When i tell you not to marry without love, I do not advise you to marry for love alone - there are many, many other things to be considered"
"first study; then approve; then love" Helen's aunt