Our neighbourhood is very friendly, and we keep an eye on each others' houses and such. But in terms of introductions, when we moved in several years ago we met all of our neighbours as they saw us in the front yard and came over to say Hello and introduce themselves. A new family just bought the house across the street from us, and there was a big "meet and greet" just before Christmas when we were all outside shoveling snow at the same time.
Re: cookies or other food. TBH, I'm pretty trusting but there is something about receiving home made food from someone I don't know (and don't know anything about) that would kind of squick me out. So if I were going to knock on someone's door and welcome them to the neighbourhood, I'd take something non-food if it seemed like a gift was appropriate. YMMV of course.