After what round of shots can I bring my puppy out?

My lab puppy is 9 weeks old and was let outside always at the breeders cause their place is desiese free but now at my house all he does is sit and stair out the big glass door to my back yard. I've heard that I could take him out un my backyard after his second shots, is that ok? Or do I need to wait until he's fully vaccinated to do that? Also I live in the country with a next door neighbor that takes very little care of their dog and their dog is probably sick. He's been through the bush/forest 1/2 of our back yard but not the grassy part so could I let my puppy play there? Sorry it's so long but thanks!! :)