I have used elgg before. It is “old” social media web site software. By old I mean both that it has been around for may years and it is just social software, not spyware. I have created sites with it before and just created a new site using it — because it is the right tool.
The site I created is pp.a42.com, a site to discuss the ideas of a book called The Plant Paradox. It is not intended to be a big site, it is what you might call a tightly targeted social site. Elgg again seems to be the right tool.
Installation and setup is trivial (copy files, set up database, run installer) and it seems to be pretty lightweight. The only thing it lacks (maybe a plugin exists for this but I didn’t see it) is a setting for admin approval of users. In the world of SPAM this is a potential problem but, for this site, as soon as the SPAM starts I will just turn off auto-login.