What is more important, society or the individual?
In God's sight every individual matters in the first place as a person and only then as a social being.
Society can never be more important than the individual person. Men may never be means to a societal end. Nevertheless, social institutions such as the State and the family are necessary for the individual; they even correspond to his nature.
How can the individual be integrated into society in such a way that he nevertheless can develop freely?
The individual can develop freely in society if the "principle of subsidiarity" is observed.
The principle of subsidiarity, which was developed as part of Catholic Social Teaching, states: What individuals can accomplish by their own initiative and efforts should not be taken from them by a higher authority. A greater and higher social institution must not take over the duties of a subordinate organization and deprive it of its competence. Its purpose, rather, is to intervene in a subsidiary fashion (thus offering help) when individuals or smaller institutions find that a task is beyond them. (YOUCAT questions 322-323)
This principle of subsidiarity was a new thing to me when I became a Catholic, and I had not since heard anything really like it articulated outside of Catholic circles. Although, looking at the Wikipedia article on it, I see it was expressed by Alexis de Tocqueville and is a principle of the European Union. Even so, I don't hear it mentioned in the news or in the political discussions I hear in the secular media.
I'm fascinated by the fact that it doesn't seem to me to really fit modern liberal or conservative camps, nor is it exactly compatible with socialism or capitalism. It supports government aid to the poor when necessary, but prefers family and community based solutions. It is definitely against centralization because individuals tend to get lost as power gets concentrated at a regional, national, or international level. However, it is also against the tendency towards a hands-off approach to social problems that you can find in some conservative and capitalist schemes.
I'll leave it to the reader to decide what political and social systems best support subsidiarity, and would be interested in any comments you might have.