We live on a small farm so I'm not a good person to answer this question. My daughter's first pets were horses, donkeys, dogs, and cats, lol.
I would say a dog would be a great way to teach your son about the responsibility, and rewards, of a pet, but if your wife isn't into the idea she may end up resenting the dog. Maybe a cat then? I think anything smaller than a cat may not teach him what he needs to know about the responsibility of having animals.