depends on what your vet suggests I imagine.
I'd say he was probably wormed enough,,(vets usually want a stool sample tho!),,if he had his first set of shots, it was most likely a puppy booster, usually around 9- 10 weeks, they are due for another, and then one more around 16 weeks,,Somewhere in between time, (again depending on location/vet) they usually do a rabies vac.
Here the protocal usually is, 3 sets of puppy boosters, rabies vac at 12 weeks, (not combined with a booster)..Again, depends on area, if they suggest a lepto booster which requires a two shot series , then yearly with the 'booster',,,(or now it's been suggested every 3 years) as well as lyme which also is a beginning two shot booster.
Here also, at one year,,they go for a 3 yr rabies, and then you go with your annual "booster"..
Have to say tho, I don't vaccinate any of my dogs anymore..
I'm sure if you have the record from the puppy owner, the vet will instruct you on his protocal for vaccines.
Good luck with your new puppy
diane