According to Dr. Laura Robinson, DVM, if you get your puppy around 8 weeks of age, you shouldn't have to worry too much about health precautions. If you do get your puppy at an earlier age, deworming is a big concern.
Typically, puppies are dewormed every few weeks up to the age of 8 weeks because they can contract parasites very easily, either from their mother's milk, in utero, or form their environment as they begin exploring the world. Setting a deworming schedule up to 8 weeks of age is an important precaution to take.
If you get your puppy when they're already at least 8 weeks of age, vaccination is the next precaution to focus on. Read more about vaccinating here.
For your first visit to the vet, it's recommended to bring a stool sample to double check for parasites. After that, your vet will likely recommend starting your puppy on a heartworm and flea & tick preventative medication.