I love Great Danes and have had 6 in the last 25 years (4 were my parents' dogs, 2 were mine as an adult). From the bottom of my heart, I would not recommend getting a puppy from a breeder who doesn't do health testing on the parents. Of my 5 deceased Great Danes, 3 died at 4 years or early from genetic issues. These were puppies that my parents got from back yard breeders, one who just bred their companion animals because they had "great personalities." These dogs ran up expenses in the many thousands of dollars each for heart issues, neurological issues, immune system issues, etc.
For my current puppy, health and soundness of temperament were the most important things to me. At a minimum, I wanted a breeder that tested heart, eyes, and hips. I also wanted a breeder who had been around long enough and was honest enough to tell me what issues she had experienced in her line, common cause of death, etc. Once I found a breeder I really liked, I got on her waitlist and also asked her for recommendation of similar breeders. I ended up getting a puppy from one of the breeders she recommended. So far Finn has been a dream, great temperament and healthy.