I think the type of media that should be featured should ideally be:
good or notable
relevant to the community
I don't think we should just add something there "because the old content has been there for a while" if we don't have anything that is bothnew and good or notable to add.
Defining good and notable
"Good or notable" means that it has to be either well done or helpful, or be something that most people would agree is worth spotlighting (e.g. maybe there's some fan art that isn't "good" by art standards, but is notable for some other reason).
Deciding what content is featured
I don't know how to do this democratically when there aren't many active members.
When there are active members we could do a poll on the main page.
Perhaps the best way is to have a forum thread and let people suggest content in there. Whatever content meets the criteria of "good or notable" and "relevant to the community" can get featured after the old content has been displayed for about a month or so.
Until we get that going (which means we'll need more active members), as one of the wiki admins, I'll just cycle in new or notable content that's relevant to the community and add it to the Featured media page.
We could let anyone do it, and anyone can indeed do it, but I have concern people will misuse the featured media box (e.g. for self promotion, ignoring the good or notable, and relevant criteria).