I spoke with a woman at the university here in Davis who studies dog genetics. When I told her I had a poodle, she said, "Is it a standard?" She told me that standards have more genetic problems (on average) than minis or toys. When I said to her that that didn't make sense to me, since the minis and toys were bred from the standards, she said that traits can be correlated in strange ways, and, apparently, some of the genetic problems in poodles were more correlated with larger size. (She also told me that people who tried to cir***vent these problems with labradoodles, etc., were just breeding one dog with genetic problems against another dog with genetic problems. Ugh).
But since there can be genetic problems in any breed, or any size of any breed, due to the inbreeding that has occurred over the centuries, your best bet is to find a breeder who does genetic testing on the sire and dam before mating them.
Speaking personally: I have a miniature who was a rescue (of a sort). I know his lineage, but I don't know the genetic history of the lineage. And I don't want to know. I figure that none of us knows how much time we have here, and I'm just going to enjoy him for as long as he is with us.
added: I think it's hilarious that I can't say "cir***vent"! Let's try "get around"