You'll want to pick a passage or two that you personally find "interesting and vivid," but I hope that I can help get you started by talking about what passages I would pick.
While many people might focus on Cather's descriptions of the landscape, I would probably focus on the descriptions of the rattlesnake in Chapter 7:
I whirled round, and there, on one of those dry gravel beds, was the biggest snake I had ever seen. ... When I turned, he was lying in long loose waves, like a letter `W.' He twitched and began to coil slowly. He was not merely a big snake, I thought--he was a circus monstrosity. His abominable muscularity, his loathsome, fluid motion, somehow made me sick. He was as thick as my leg, and looked as if millstones couldn't crush the disgusting vitality out of him. He lifted his hideous little head, and rattled.
My big rattler was old, and had led too easy a life; there was not much fight in him. He had probably lived there for years, with a fat prairie-dog for breakfast whenever he felt like it, a sheltered home, even an owl-feather bed, perhaps, and he had forgot that the world doesn't owe rattlers a living. ... So in reality it was a mock adventure; the game was fixed for me by chance, as it probably was for many a dragon-slayer. I had been adequately armed by Russian Peter; the snake was old and lazy; and I had Antonia beside me, to appreciate and admire.
I like these descriptions of the rattlesnake because they show two very different ways of looking at the same creature. The first description (from the moment the contact with the snake occurs) emphasizes monstrosity, perhaps even uses vaguely sexual language, and the second (from a much later moment, when reason has replaced excitement) emphasis a sort of helplessness of the snake.
Another description that intrigues me everytime I read the novel is that of the conductor in Chapter 1:
Beyond Chicago we were under the protection of a friendly passenger conductor, who knew all about the country to which we were going and gave us a great deal of advice in exchange for our confidence. He seemed to us an experienced and worldly man who had been almost everywhere; in his conversation he threw out lightly the names of distant states and cities. He wore the rings and pins and badges of different fraternal orders to which he belonged. Even his cuff-buttons were engraved with hieroglyphics, and he was more inscribed than an Egyptian obelisk.
He is a sort of magical figure, a guardian or guide for Jim as the boy journeys into an entirely new world.