Would a minor in business or finance be more helpful for a veterinarian?

Yes. An understanding of business principles is critical for any field of study. I would recommend a minor in the field of business to round out your studies.

I must agree with my tocayo or name twin that indeed a good understanding of how to run a veterinary business would be very beneficial. Perhaps during this learning you can also move towards a financial type background. You could study both however I believe it would be very advantageous to learn as much about how to get that vet business rolling to help all animals as well as oneself along with family & friends.