Consider medical concerns that may come with a specific cat. If you have your eye on one cat in particular, ask about it's medical history to see if it requires any long-term care. Would you be able to afford this cat's medical needs?
Even if the cat is healthy, consider its breed. Purebred cats from different breeds can have their own genetic problems to overcome. For example, flat-faced cats like Manx and Scottish folds often develop breathing problems.[2]
Purebred cats are more likely to have genetic medical problems than non-pedigreed cats.[3]