The consumer socialization process is a very broad topic, so depending on what interests you, almost any method could be used to study some aspect of that issue.
In general, the choice of a method is driven by a research question, so can you say more about what you want to study with regard to this topic?
I agree with David. Consumer socialization, being such a broad field of study, you could use qualitative, quantitative or mixed methods. However I recommend you consider the following:
1) If you have not defined your research question accurately. In this case, you should advance in the literature review. A qualitative approach is also possible in this state of things. As you progress in qualitative field work (e.g. in-depth interviews, focus groups), you may continue to delve deeper into the past literature.
2) If you have already defined your research question accurately. You would follow a qualitative or quantitative approach. In the latter case, you should have raised your hypotheses before designing your data collection instrument (e.j. questionnaire).
One last tip. If the specific topic within consumer socialization you are interested in is well studied (by past research), it is better to go into a quantitative approach, because you have support (in the literature) to pose hypotheses. On the other hand, if the specific topic you want to study previously has been little tackled, perhaps the qualitative approach is more profitable.
First of all thank you very much for the answers and tips. I am advancing in literature review and have a few ideas for further investigations. I am especially interested in the influencing factors and would like to know how they work in the case of families with different social or demographic background. I am also hesitating wich family member should be investigated, as different actors can have different point of views.
The easiest way is to go for quantitative way, surveys with the standardized questions works good. If the respondents are specific (kids for example) you may consider qualitative ways like interview or observation.
It sounds like you are developing a "variable-oriented" approach, which would be a good match to survey research. If so, you would need to separate independent variables from dependent variables, and you would need to operationalize both.
If you do not have measures for your key constructs, then a qualitative study should help you to do so. This could either be your main study or part of an exploratory sequential design in mixed methods ( qual --> QUANT).
Another factor is that survey research requires you to develop a sample, often with 200 or more respondents to have enough "power" to do statistical tests.