Currently when a user goes to the Chatter tab, the default view is "What I follow". This is causing my users to accidentally post outside of specific groups. Is it possible to make users default to a certain group for posting? Would this require a Visualforce page?
You could create a WebTab which points to the URL of the Group that you want to post to. You could set this tab as the default landing tab for the App that is assigned to your User's profiles. (You could also consider getting rid of the default Chatter tab from the App that is assigned to the Profile, to avoid any confusion)