Free CMS with user pages, surveys, calendar, wiki, activity log, email, login-protected pages visible by all or some users

Question

I am planning a tabletop RPG campaign. Due to the way I want to run it, I am hoping to set up a website for it.

Requirements*:

• Free - at least for the end users, but I also would rather not pay when I can host my own site
• User management - create accounts, set roles/privileges
• User specific pages - each user would have a profile page and be able to create x "character" pages
• Login protected pages - some pages will only be visible to logged in users (some potentially only to specific users)
• Surveys - mostly for gathering feedback
• A calendar of some sort - For being able to plan out meeting times
• Wiki - for tracking people/places/things
• Some sort of log/journal - Ideally allowing certain specific users to edit
• Email
• Up and running fast - The sooner I can get it running, the better (main reason I am avoiding building from scratch)

I started working on implementing this through a self-hosted Wordpress site, figuring that I could get most of the functionality out of plugins and create my own custom plugin to cover the rest. But the more I work on it the more I feel like it's becoming a Frankenstein's monster of plugins and custom code, and that Wordpress maybe isn't the best option.

Question(s):
Is there a good (small) set of plugins for Wordpress that can cover my needs?
Is there a better (self-hosted) CMS that would be a better fit? Or am I better off just writing this whole thing from scratch in something like PHP or node?

*Not all hard requirements, but the more that can be ticked off the list, the better.