Community is perhaps more intimately connected than "society." By "intimate" I mean a community is interdependent for survival...pretty much a team effort where no member can be left out of the daily activities in order for the group to function as a whole. In a society, the members are less dependent on each other for individual survival, and therefore are more free to experiment and contribute to non essential activities such as the arts, sports and recreation, and inventing new technologies. When people have more leisure time, (i.e. not having to spend most of their time gathering food and water, building shelter, defending themselves etc...), they tend to take on more and more complexity to their lives thus giving rise to an increasingly more diverse culture...a society. Well this is how I would differentiate the two anyway.
This is the basic position of Childes' thesis; as the community settles(aquires more things) and gets more organized (division of labor: specialists) we see what you describe.I think community and society are just the steps intermediate to civilization (so-called); I used a lesson based on this when I taught world history.
By all definitions so far supplied, civilization is desirable, but not yet achieved. It is a good idea, though. Maybe it will come to be sometime in the future, long after I am dead. To me, the bottom line is peace among all peoples. Sadly, we fall far short, so I don't think civilization is so hot right now.