Hi and welcome
I think this is a concern and issue to think about with ANY breed of dog, even a "mut". The common problems associated with Yorkies has already been mentioned, but every breed has it's "issues".
The best thing you can do for ANY dog is prevetative care and a great diet. You want to start researching high quality foods now so you know what you'll start with (unless the breeder has a recomendation, but I've heard some supposable "good breeders" recommend some rediculous things).
As with any animal or human for that matter, good health comes down to taking care of yourself. "You are what you eat" really is true
.
Other than a holistic food, a great vet who doesn't overvaccinate and proactive care (ie. wellness exams and not allowing things like crazy jumping) it's comes down to breeding and the rest is chance.
What I did after I had to unexpectedly dish out $450 for my cat to have emergency surgery 4 weeks before my wedding
, I started a "pet savings account". I started out by putting $100 in there and I add between $5 - $30 each week to it. It's small so far, but we don't miss that little bit each week, it gains interest and I know it's there if we have an emergency. There's also the option of pet health insurance (alot of people here like Trupanion insurance) if you can spare about $30 or so a month for the premium (I personaly prefer the saving account, but it's a personal choice).
Bottom line, with any pet there's the possibility of having an unforseen expensive problem and the only way to
possibly avoid breed specific health concerns is to adopt a mixed breed, but that's of course not a guarantee either.
You don't have to be rich to own a dog, but you do have to be prepared