Just my personal preference, but I think a shelter pet is the way to go - it’s where we’ve always gotten our cats. I’ve heard that mixed breeds have better genes. Besides, you’re rescuing an animal that might wind up being destroyed!
Mixed breeds are much better genetic-wise.
In dogs, Dalmatians tend to have hearing problems. Large Golden Retrievers tend to have lower back and hip problems.
Other breeds have a high likelihood of certain blood-borne diseases.
A mixed breed would probably be healthier, live longer, cost less in vet bills, and in general not be as high-maintenance as a purebred.