Adopt or Shop

Buying a puppy

Pros:
You get all the fun of puppy zoomies, puppy breath and irresistible cuteness
You can start off the training from Day 1 in the way you want to train, thus (hopefully) avoiding long-term issues
Puppies are fun!!!
If you choose the breeder carefully, you have a good chance of avoiding long-term health issues and dodgy temperament (you want a breeder who has selected for temperament, not just appearance)

Cons:
Everything can get chewed: chairlegs, cushions, pens, shoes, your hands and ankles...
Housetraining 'accidents'
Having to take pup out every hour or even more often when housetraining
Puppies can be as much work as a human baby - more, in fact because if you put a baby down it stays where you put it and doesn't try to eat everything in its reach
Broken nights
More expensive
Will need to have someone there just about all the time to start out with

Adopting an adult

Pros:
Cheaper (at least in the short term)
If you adopt from a good rescue, you know a lot about the dog's temperament, training and behaviour
Possibly already housetrained
You are giving an unwanted dog a good home (and making space in the rescue for another unwanted dog) - you are literally saving a dog's life
Probably much less work
If a crossbreed, may be healthier than your average pedigree dog

Cons:
You are unlikely to know the parentage and any issues the parents had
May have been abused in the past and as a result be scared of (and fear aggressive towards)anything from men wearing hats to gates (someone I know has adopted a dog with a strong fear of gates...
May well have been poorly socialised which can also cause fear of certain people, dog reactivity, etc.
May not be housetrained and will have bigger 'accidents' than a pup
May not have had any training at all, and training will take longer than with a pup
May be 'shut down' in the rescue so their personality may not appear until a few weeks after you adopt them
May even be so traumatised that they can never be 'fixed'
Will take longer to build a bond and mutual trust

I'm sure there's more pros & cons to both I've missed. Most of the risks of adoption can be avoided if you choose a good rescue organisation. Bear in mind that though some people say you should never buy from a breeder while there are dogs in rescue, if no one bought pups from good breeders, before long all dogs would come from puppy farms, bad breeders and random accidental matings - and because they will probably develop health and behavioural issues because of bad breeding or early experiences, are much more likely to end up in rescues. So ignore anyone who says that you 'must' adopt and make your own decision.