The quotation you choose depends on which theme you decide to focus on. The eNotes study guide tells us that the themes of the story are death, the decline of the old south, and community vs. isolation. Try these:
For the theme of death:
Being left alone, and a pauper, she had become humanized. Now she too would know the old thrill and the old despair of a penny more or less.
For the decline of the old south:
It was a big, squarish frame house that had once been white, decorated with cupolas and spires and scrolled balconies in the heavily lightsome style of the seventies [1870s], set on what had once been our most select street. But garages and cotton gins and encroached and obliterated eventhe august names of that neighborhood; only Miss Emily's house was left, lifting its stubborn and coquettish decay above the cotton wagons and the gasoline pumps--an eyesore among eyesores.
For community vs. isolation:
And that was the last we saw of Homer Barron. And of Miss Emily for some time. The Negro man wentin and out with the market basket, but the front door remained closed. Now and then we would see her at a window for a moment...but for almost six months she did not appear on the streets. Then we knew that this was to be expected too; as if that quality of her father which had thwarted her woman's life so many times had been too virulent and too furious to die.
I hope these help!
How about a sequence of lines from near the end of the second section?
"We did not say she was crazy then. We believed she had to do that. We remembered all the young men her father had driven away, and we knew that with nothing left, she would have to cling to that which had robbed her, as people will."
This quotation gives you the town speaking with a single voice, and making excuses for Miss Emily. It gives you her history, as publicly known, and the last sentence indicates that in the world she lived in, clinging to the dead man made a kind of emotional sense.
The narrator explains that the townspeople "had long thought of [Miss Emily and her father] as a tableau; Miss Emily a slender figure in white in the background, her father a spraddled silhouette in the foreground, his back to her and clutching a horsewhip, the two of them framed by the backflung front door."
This detailed image encapsulates the identities of Miss Emily Grierson and her father: they are separate from and yet consider themselves superior to the rest of the town. Miss Emily, however, is still overshadowed by her father; she remains "in the background" of her own life even after his death.