Rhetorical choices is another way of saying language choices, so what you're asking is how does that author's purpose impact the language in the text. One really great speech to illustrate this point is Jonathan Edwards' speech "Sinners in the Hands of an Angry God." It's very easy to see from the very beginning that is purpose is to convince his audience that they are in grave and mortal danger because the sins they commit. His language choices are clear and very intentionally made: one image he gives to his listeners is that God's wrath is like a bow bent and ready to strike. He also explains to listeners how many people are already suffering in Hell for all eternity and that the only reason they themselves aren't already plunged into hell is by the hands of God - any angry God that they insult daily by their sins. These images and language choices directly correlate to his purpose. He is trying to persuade, but not just any argument - one that (he believes) has a life or death implication.
Think about how his choices might be different if his purpose were just to inform. His language probably wouldn't be quite so fiery or his tone so urgent. An author's word choice is always purposeful and full of thought. When you identify his purpose, it's easy to pick out what he chose certain images or words in his writing.
The author's purpose is basically to inform, persuade, or entertain, although authors have more specific goals while writing, and the specific goals that the author has will influence his or her rhetorical choices. Authors will use different rhetorical strategies depending on how they would like to impact their audience. A politician, a small business owner, and a waitress can all write pieces about the minimum wage, but because their opinions about the subject and their purposes for writing are different, the rhetorical appeals they would use would also differ.
Molly Mayor, writing a speech about minimum wage, hopes to get the public's vote, so she would be concerned about making sure that the audience trusts her. Molly would use ethos, or an appeal to ethics, to convince the voters that she is honorable and trustworthy. Molly needs to convince the voters that she cares more about the well-being of the population and the city than her own personal interests.
Betty Business-owner, writing an editorial about minimum wage, hopes to keep her business costs down so she can keep her doors open. Betty would use logos, or an appeal to logic, to convince her fellow citizens that raising the minimum wage would hurt the community. If business costs go up, then prices go up, which hurts consumers, or businesses close, which hurts consumers. Molly needs to convince her neighbors that, logically, they will be negatively affected if the minimum wage is increased.
Wanda Waitress, writing a blog post about minimum wage, hopes to raise her income so she can work fewer hours and spend more time with her kid. Wanda would use pathos, or an appeal to emotions, to convince her fellow citizens that raising the minimum wage is the right thing to do to help the people who are less fortunate. Wanda needs to convince her readers that they can make the world a better place with their compassion.
Ideally, an author would be able to use a combination of different types of rhetorical strategies, but the ultimate goal helps the author make rhetorical choices.