Since others have already said most of what I would say, I will take a slightly different aspect of this. Development is influenced by the stability of the relationships when a child grows. In other words, development can be stunted by instability or a lack of relationships. A loving home, with healthy relationships, allows for steady and normal development. In its absence, abnormal development results.
We grow up modeling the behavior of those around us, at home and out in the world. We generally adopt the values we are taught and observe in action--at least for a while. Whether they become a permanent part of us, however, depends on other influences.
Young people, especially those who do not have strong, loving relationships within their families, often reject the behavior and values they have learned at home. They declare their independence by adopting very different ways of thinking and behavior. Their development is influenced by their families, but in an ironic way.
In terms of peer groups, some young people are strongly influenced by their peers, while others go their own way. They will ignore or reject the prevailing peer group thinking/behavior, often finding other individuals who have defined their own values.
Family, peer groups, and culture are strong influences in a person's development, but they do not always determine who we become. An interesting subject is to consider why some young people grow up to define their own values and think independently, while others continue to model the thinking and behavior of those around them, without question.
In response to ask996, I have seen students both rise to a higher level and sink to the lower level. I would agree that most of them tend to sink to the lower level, simply because it is easier to do so. I also agree that our family has the most influence on us and our development.
Something that we might consider is whether the affect these groups have on us becomes part of our nature or merely habit. Observations of students in a high school classroom will typically show that students tend to adopt the same behaviors as the friends with whom they associate in class. However, these adaption of behaviors is usually a regression. For example it seems as if more students lower their level of effort to fit in rather than other students raising their level of effort to fit in.
Clearly both psychologists and sociologists have recognised the massive impact of the three elements you have identified on the development or formation of an individual's norms and values, or their world view. Of course, from the moment we are born, this process begins, and is referred to as socialisation. We take in so much of who we are from our family, then our peers as we become older and more independent.
I think those three aspects are listed in the correct order of importance as far as socialization goes. Family has by far the most influence in social development, and usually involves the strongest social bonds, and the most long term ones. Daily contact makes a difference too. Peer groups, in my opinion, refine that socialization, and culture reinforces it over time.
For one thing, the more that you are encouraged (by family, peer group or culture) to act in certain ways, the more you are likely to act in those ways. For example, if you go through your childhood with an older brother who tries to do everything for you, you may get the idea that you are incapable of doing things for yourself. This may stunt your development in those areas in which he tends to take over (like if he is always fixing things for you instead of letting you do it yourself, you may never develop mechanical aptitude that you might otherwise have developed).