Because your puppy gets antibodies from nursing which will interfere with vaccinations given too early, he shouldn't get his first shots before 9-10 weeks old. He should get his final vaccinations between 16-18 weeks as they should be able to provide full immunity by then.
A study of a cross section of different puppies showed that the age at which they were able to respond to a vaccine and develop protection (become immunized) covered a wide period of time. At six weeks of age, 25% of the puppies could be immunized. At 9 weeks, 40% of the puppies were able to respond to the vaccine and were protected. The number increased to 60% by 16 weeks, and by 18 weeks, 95% of the puppies could be immunized. Maternal Immunity: Passive Disease Protection from the Mother in Dogs
You must wait for two weeks after he has had his last vaccinations for full immunity before taking him to public doggie places like pet stores, dog parks, grooming salons, etc.