You and your dog should train together. Even if you have taught your dog all of the relevant commands at home, you should take the chance to expose him to all kinds of new people and other dogs in a class. A lot of dog training is actually owner training, and a good instructor can point out places where you can change your approach to have a more socialized and manageable dog. A good trainer can also be invaluable in giving you tips on how to manage any kind of problem behavior you may run into.
As you live with your dog, you will get a handle on just how much you want to require from him in terms of behavior, and how interested you may get in various kinds of training venues (there is more than just obedience out there---nosework, tracking, agility, rally.......) that could lead you into different classes and activities.
But all dogs should learn things like sit, down and stay, to walk calmly on a loose leash, to be non-aggressive toward strange dogs on leash and people who pass by on a walk, to settle down calmly in the house, potty training of course, to control his chewing and destruction urges, to be OK with being alone in the house while his people run errands or work.....
Strictness is not quite the word I would use for living with a dog....consistency is a better term. If you don't want a certain behavior in your adult dog, don't let your puppy indulge in that behavior. If it is not OK for him to pull on the leash, it is never OK for him to pull on the leash. If you don't want him on the couch, he should never be on the couch. Set your rules...you stick to them too.
You need to make special efforts to reward good behavior (by food, play with toys, praise....). You do need to let him know when his behavior is unacceptable, but (especially with a puppy) that can mean something like giving him alternatives (sit instead of jumping up; chew on this toy, not me) or depriving him of your attention (if you're going to be bitey, pup, you can stay in another (puppy-proofed) room for a couple of minutes until you calm yourself down).
I would tell a person wanting a dog to do some thinking about exactly what they expect from their dog, and whether they can meet the specific needs of a particular breed. I would advise them to research different breeds and visit with owners of a breed they think they might match well with. To read a little bit about dog behavior so they can figure out what makes their dog tick, and what methods would work to teach them what they need to know. A basic puppy class to work on socialization and get you started on the right foot when it comes to teaching living skills to your puppy, and a basic obedience class to teach leash manners and the basic commands would be the minimum formal training I would recommend.