Private lessons can be a terrific way to help someone get started with training, especially when there is a need for concentrated work on specific issues such as separation anxiety, fear, or aggression. But, even for new puppy parents, we often suggest a private lesson or two prior to enrolling in a puppy kindergarten class. This way they can get started with effective management, handling exercises and teaching manners asap.
One of the positives of private lessons, working in a fairly non-distracting environment, may eventually become a bit of a drawback. Once the dog/handler team has developed a good training foundation, working in a classroom setting around other dogs and their people can be a superb way to begin to practice around a variety of distractions that are still somewhat controlled.