I'm trying here to give a summary answer to get started with the various points you mentioned. Of course more detailed answers can be found for these specific topics elsewhere on pets.SE.
What about the breeder?
This doesn't apply if you're getting a rescue dog.
A good breeder should give you full access to his installations before you adopt the puppy. You should also be able to see the mother (unless specific cases where you adopt an older puppy and the mother is no more around) and should be able to "test" the mother: can you approach her (not a straight ahead approach especially if she's with the litter, the breeder should show you how to proceed), can you pet her, etc. Usually you'll get much less information for the father but the breeder should at least able to tell you his story.
If you adopt a pedigree dog, you should check carefully the documents of the mother and the father (at least, usually you can easily go up one more generation). This depends from country to country.
The vet will probably have seen the puppies once or twice. Again depending on the country you should receive a wellness certificate. A few days after adopting the puppy you should go see your vet, show him the report from the other vet and make sure that everyone agrees with the well being of the pup.
How can I find out if a dog I am considering is from a puppy mill?
What about the puppy?
Female or male will probably not be spayed/neutered at that age. See other questions on this site about the best age to neuter a male dog.
Young puppies won't be completely house trained and will not bark in any case. House training is not rocked science and starts with the mother. After 3 weeks the mother doesn't trigger elimination by licking the belly/genital area, so the pup will go in the litter. He will be "pushed" by his mother and he will learn not to soil his sleeping area. That a very good start for you as you will complete the house training by "locking" him in a crate or very small area of the house at the beginning. With a lot of prevention you'll avoid accidents and you will also praise him a lot for going outside. Then by yourself a tablet of Xanax and wait calmly until his house training is perfect.
Depending on the breed you'll focus the veterinary information on genetic diseases, hip displasya is a major problem, read more about that in other questions.
How old should a puppy be whenever you adopt them?
How do I spot potential problem behavior when adopting a dog?
How to approach a dog for the first time?
...All questions referencing puppies.
What about food?
Obtaining a clear and scientific vision of what dogs should eat is starting point of many heated debates. Concerning your puppy I would focus on a few points:
- When you adopt the puppy, at 8 weeks of age, he should be eating (almost) exclusively solid food. If the breeder tells you otherwise, see with your vet.
- You have time to decide what your puppy will eat as an adult. Usual commercial kibble might not be your final choice, but there is no reason to panic: many dogs live perfectly well and in good health on that food.
- Diets that you should consider for your adult dog are: entirely raw meat diet, entirely raw bones diet, home cooked diet (with varying percentage of meat), dry kibble and wet kibble. You can mix them all: my dog has dry kibble in the morning, home cooked stew in the evening and bones when left alone.
- If you change from the breeder's food to your own brand, do it progressively. Puppies' digestive tracks are sensitive.
How much should I feed my puppy?
What should I monitor while changing my dog's diet?
....All questions relating to dog food and dog's diets.
What about general training?
You will have to choose a training method. This leads to even more heated debates than the choice of food. The problem is that some methods can physically and quickly hurt the dog, much faster than eating a crappy kibble for example.
It is now established scientifically, by various and independent group of people, that any training can be done using positive reinforcement and negative punishment.
How can one judge the quality of puppy classes?
How to stop dog chewing things
How do I stop my dog from barking at random strangers
...All questions related to training dogs