I would steer clear of building anything yourself, if you can possibly avoid it. WordPress is relatively easy to set up and maintain, but:
The problem with creating yet another platform is that it is yet another platform and it can be difficult to generate enough interest to keep it alive
In my experience, this is the key point. FB is successful because lots of people use it already and it pushes updates and events out to the users; they don’t have to actively choose to go and visit yet another website to find out what is happening. People can post snippets of information quickly without having to remember another login and use a CMS.
You could consider using a FB Page, rather than a Group. Pages can be public, so you don’t have to sign up to FB to view the information on them.
I don’t have a FB account and have no interest in using it, but in my experience of developing online resources for a club, you’ll get a lot more interaction via FB or one of the other existing social media tools than you will through a custom built website.