I believe they learn important things from their mother between 6 and 8 weeks though.. I would trust the more experience people of the forums about it personally.
Fran27, The breeder of my Newfoundland dogs. She has large breed dogs (Newfoundland dogs), she takes the mother away from the pups at the age of 3 1/2 weeks. This is due to the mother being large and the breeder having to stay with the mom and pups to constantly supervise that the pups are not stepped on in error. the pups begin being weaned at about 3 weeks and mom is just brought back for nursing while they are being put on solid food at around 4 weeks. These pups turn out fantastic and are more focused on human companionship, they have no shyness or fears because they have been properly socilaized by the breeder. I also have a female Newf that was kept with the mother, she is a nervous wreck and it took me years to overcome her fearfulness etc. her problem is probably more genetic, but, the breeding was repeated and all the pups were taken away earlier than my fearful Newf and they turned out wonderful. BTW, my fearful Newf is a champion in USA and Canada.
When I was growing up all of our pups were given to us at the age of about 5 - 6 weeks. We took the pup's every were and they got the socialization they required, they were the best dogs a child could have owned. One being a Shepherd/Husky mix the other a Border Collie/Lab mix...they were trustworthy, and could handle themselves in any situation. The age we adopted them did not affect thier future manners. I have seen just as many freaky and fearful pups that were kept with the mother and other pups, perhaps more. And I see it A LOT more in inbred mixed breeds (purebred dogs) than I have seen in natural breeds or mixed breeds...although I have seen my fair share in the latter as well.
I believe a lot has to do with the new owner of the pup and how well they do socializing the pup.
you can always find puppy play groups for your pup to join. At least in my area we have little groups for young pups after their first jab where there is an obedience instructer there just to over see every thing and help the puppy owners.
As far as genetic testing, I have seen the best dogs get all cert's and still produce pups that have HD and other genetic disorder. Genetic disease are caused by purebred breeding and even in clean tested lines you can still produce genetic disasters, I see it all the time. One litter of Bull Mastiff's from genetically clean lines (tested for every thing) were so bad off the breeder had to euthanize the whole litter. So, genetic testing is no garantee, and even a dog that clears at 2 years of age can still get HD or ED latter in life.
Many reputable breeders are saving themselves from refunds etc. by writing in the gaurantee "so long as the dog can still function as a pet".
Good luck with your new pup.