Hi there,
Did you not get information from the breeder as to when your puppy was due to be wormed? Most "good" breeders will provide you full details of what wormer was used and when they are next due to be wormed.
Its hard to give advice without knowing what treatment for worms has already been given. I would discuss with your vet when you take your pup for vaccinations. And yes, your adult dog should be wormed at least 6 monthly with a good quality wormer (not one you buy in supermarkets but one from your vet).
Hope this helps