What kind of questions should I be asking to impress?
I think a better way to think of this opportunity is,
What kind of questions should I ask in order to make sure I'm entering into an employment arrangement that will be mutually beneficial?
In other words, think of the interview as a two way street. The employer wants to evaluate your fitness for the job, but you should also be evaluating the employer in terms of your own preferences, motivations, and desired work culture. So - rather than trying to ask questions that will sound impressive, spend some time thinking about what's important to you, and then ask questions about that.
If you're interested in growing a certain skill, or you find certain types of work the most rewarding, ask questions about those factors. If you're interested in advancement, ask about their policies around internal promotions. You mentioned interviewing at a vet - maybe you want to ask clarifications around the time you'll spend interacting with the public/animals entering the clinic, vs "back room" admin work - if that's important to you.
It's also good to ask clarifying questions about what you'll be doing in the day to day functions for the job, if that wasn't obvious from the job description. And, as most people are looking for some degree of long term relationship, it's reasonable to want to know about the company's future - how are they growing or changing over time?
The bottom line is, the employer is asking you questions to determine if they want to hire you. They have thought about what kind of candidate they want, and they're trying to determine if you're that person. You should take the same approach - think about what's important to you in a workplace and a job, and ask questions about those things.