Having the power to "baby a puppy" you just took home because its so tiny and adorable can be very tempting. But you have to remember that by doing so, this may lead to an untrained pup and a spoiled dog that will have a lot of different behavior problems in the long run. If this is the case, it will be hard to retrain a dog if he's already aged and is used to certain patterns already.
Dog leash training is one of these behavioral issues. When the dog is still a puppy it would be best to train them with a leash as they are still small and are easy to control. It is harder to train an older dog with the leash as they are heavier and will be more able to pull the owner around and cause troubles.