For the health and wellbeing of your dog, training should really not ever be considered an option when owning a dog. Well trained dogs are more likely to be behaved and listen, be void of behavioral issues, be good in public, and are less likely to bite. Owners also have a much closer connection with the dog when the time is taken to form a relationship through training.
The personality of a dog is flexible and indeterminate. Dogs can be exuberant or shy; friendly or hostile; fearful or bold; aggressive or passive or some combination of the above. These differences in personality may to some extent be determined by breed, or individual genetics, but for the most part it is based on how and to what extent each particular dog has been socialized.
Having a dog has been a fun and wonderful experience for everyone in your family. In fact, it has been so rewarding that you are now seriously thinking of getting a second dog. However, it is important that you really think this decision through, because having two dogs can be an entirely different experience from having one.