If you make the decision on which pup goes with which familiy, how do you decide? For example, Alpha pup goes with what type family? Less confident pup goes with what type family? etc.

While we ultimately let our families pick their own puppy, we do give them guidance and we've never had anyone disagree with us on which pup was right for them. We train hunting dogs and to start, we divide our families into those that want a hunting dog and those that want a pet. The puppies that show more drive when introduced to birds and bumpers are the ones we steer the pet people away from. If I've got a litter that is primarily going to pet homes, I would always put a strong alpha pup with someone who has dog experience and knows how to handle it. We spend a lot of time with our pups and know each of their personalities well, so our goal is to match each puppy with the family who is looking for that type of pup.

Early on in my breeding career I had puppies from a litter temperament-tested according to the standard test found in books on temperament (also see the ATTS - more for protection breeds but gives some good info). This test was given by Enid Bloome of Winterset Labradors, (many of the long-timers remember her) a lady who put multiple titles on her dogs (advanced obedience, championships and working test titles - her husband Selwyn was an avid hunter) so she knew quite a bit about temperaments.
What she saw in the pups was exactly what my husband and I were seeing in the litter. We noticed the subtle differences - the one who was first to jump out the door to the outside vs the one who had to be coaxed, etc. The tests showed what we already knew about the pups.

As far as matching up homes, I use a 2 page questionnaire that grills the families about their needs, wants and household. I use this information to match pup to home. You don't want to place a hesitant, quiet pup with a houseful of rowdy boys, and neither do you want to place your boldest pup with the retired couple that just want to have a calm companion or with a first-time dog-owning family (unless they have rowdy kids - but choosing families are another story!).
I make sure I meet everyone in the family, including grandma and grandpa if they live there, and even the au pair. Using this system I've had only one mismatch and that lady misrepresented herself (she said she wanted a dog for competition obedience when she really wanted a TRAINABLE dog, big difference!). I tried to get her back, but they worked with a professional trainer at home (who told them that the family was the problem, and the dog was great - really easy to train!) so they were able to work things out.
Hope this helps!