I think that having a Discord would be the perfect way to discuss the server outside of global. It's a lot more convenient than teamspeak, it has voice and text channels which are separated from eachother, and I just like it more since it's pretty much my main method of communication aside form Skype. I've seen Discord servers opened up for different Minecraft servers and even some game developers (Chucklefish, the creators of Starbound for an example).
It doesn't require your own dedicated server to set one up as well, as it's run on their own server that they use for their website.
Don't really know what else to say about it, really. Get a Discord. It's great.