should I make a social media page or a group?

A Facebook page or other social media page is like a blog. You can write directly to a certain group of people or directly to a group of fans or whatever. But it's different from a group. For example, if I had a band and I wanted to talk to the fans directly I might make a page to do that. But if I wanted to make a group for fans of horror movies, I might have more success with a group or club. Say I wanted to talk to someone about the latest Marvel movie. A group for movie fans might be the better place to do that. you are more likely to get reactions in a group. whereas page readers might never respond to a post other than liking it. you're much more likely to get a respone from the group members. a couple of my pages are successful in that they have a lot of followers and get reactions to their posts. That's what you want from a page or group and if you don't get reactions or comments you just might lose interest in pursuing the project any further. 

in other words, a page is like a blog where you can talk to or tell stories to it's readers, but a group is more like a chat room, where fans can start a discussion or react to another one. you have more control over a page and can keep it out of the gutter, where as a group or club is more of a group effort. 

Do you want people to talk back to you or do you want to tell them your stories?