The concept of the 'All American Man' can mostly be identified with the middle-class white male in his 30s or 40s living in the suburbs, often accompanied with a wife and two or three children.
One notable similarity behind most of the fathers in this picture is the fact that they wear formal suits, white shirts or sweater vests and are almost always tucked in to maintain this formal and middle-class, clean look about them.
The art and style would very much need to resemble the kind of art style that was being used in animation in the 50s. Knowing this, I also searched through 50s western animation, stumbling upon this image gallery of 50s commercial art in the process: http://theimaginaryworld.com/rayart.html
The gallery's images, likewise with the photos of the 'American Family' all have one thing in common: the characters are very simple in design, but also very stylized. This also reminded me of one particular aspect of a certain game that's become very widely known:
This is the 'Vault Boy' seen throughout the game and the unofficial mascot of the Fallout games. This simplistic style is very similar to the style of 50s animation and the fact that the story and style of the Fallout series takes a lot of inspiration from the 1950s.
"The series is set in a United States alternate history scenario which diverges from reality following World War II. The transistor was not invented, while vacuum tubes and atomic physics became the cornerstones to scientific progress, eventually achieving the technological aspirations of the early Atomic Age and locking society into a 1950s cultural stasis. Thus, in this alternative "Golden Age", a bizarre socio-technological status quo emerges, in which advanced robots, nuclear-powered cars, directed-energy weapons and other futuristic technologies are seen alongside 1950s-era computers and telephones, and the aesthetics and Cold War paranoia of the 1950s continue to dominate the American lifestyle well into the 21st century." (Wikipedia)
In my opinion, we would do well to incorporate this type of style into our character design as well as our art style as a whole.