The non-core vaccines (at least the ones that we administer here) are leptospirosis and bordetella. We especially recommend the bordetella vaccine for dogs that go to dog parks or boarding facilities. That's for kennel cough, which is a respiratory condition. And then leptospirosis is a bacterium they can get out in the environment, especially around water, and that can really affect their kidneys. So we'll vaccinate against that.

Core vaccines are the ones that should be given to every puppy regardless of their lifestyle, regardless of what your intentions with that dog are. And I'll explain a little bit better. So core, again, parvo, distemper. Every dog should get those ones.
At the same time, there are things called non-core vaccines, and those are a little bit more dependent on what your dog's lifestyle is. Two examples I can think of right out of the gate, one is leptospirosis. Leptospirosis is usually a bacterial disease picked up from rodents. Well, if your dog's never out in the field or in places where rodents seem to frequent, you might argue that that one's non-core. Do I give it to my dogs? Yeah, but they're outside hunting with me quite a bit.
Another one is Lyme disease. Depending on where you live and how outdoorsy, so to speak, your dogs are, maybe that's not a core vaccine. The only way they get exposed to Lyme is if they're exposed to a tick who carries it and that's in certain regions of the country and outdoors, so that would be considered a non-core vaccine.

The core vaccines are DATPP, distemper, adenovirus, parvo, and parainfluenza, and rabies. There are some other non-core vaccines that we recommend later on.

From day one, your puppy should absolutely receive what's called DATPP. That's distemper, adenovirus, parainfluenza, and parvovirus. And from then, every three weeks, they'll receive that same vaccine, plus some later on.

Well, most vaccinations for puppies come in a combination, and the big ones that most people are familiar with and are probably still the most important are distemper virus and parvovirus. That doesn't mean that those are the only two that your dog needs because there are other things like coronavirus, not the same one, a different canine coronavirus, hepatitis, leptospirosis. Those are all things that can be included as well. But distemper and parvo are probably the two most common that we still do see from time to time in practice on young, unvaccinated puppies. So, I think those are the most important ones.

Just exposure early and often is the best way. I don't have a formula. Every dog is different. But it's just exposure. Start with a leash so you have them under control. You don't know how those other animals are going to react. So do it in a controlled setting where they're both leashed, but start small. 
If one or both of the dogs are either acting aggressively or perhaps the other way, being very fearful, do it very matter of factly. Just take them for a walk and let them get close to each other, but keep on walking. And then as they get comfortable and they realize it's no big deal, maybe then you make another pass and they get a little closer. Or maybe you stop and talk with the owner. Try to mimic a normal day-to-day situation that you might run into.
Start early. Do it often. If you can implement any of this, trust me, you will be happier for it, and you're going to have a much better, well-rounded dog when it comes right down to it.