The miniature schnauzer, toward which you seem be leaning, is a nice breed, too. I have known some, however, that have been barkers. And they do need periodic grooming to look their best. They're a nice size and would, I think, be a much better choice than a wire-haired fox terrier. I'm sure you understand that any puppy needs a lot of time, training and patience to become the pet you desire.
Obedience training can help any dog, though some are easier to train than others.
Terriers tend to have a mind of their own, which makes them a bit more resistant to obedience training than other breeds. But I think it's important for these breeds to have the chance to socialize with other dogs in the class and learn to accept them. However, an owner must be motivated and willing to work with the dog. If you take your dog to obedience classes once a week, but seldom or never work with the dog at home, you will not see the change in your dog you hope to see. So motivation on the part of the owner is the key to success.