You don't run a forum on apache alone, you need a php and mysql install too. You aren't going to need phpmyadmin unless you're directly working on the database or for initial install. I used phpmyadmin for my first install but I do it correctly these days.
Simple Machine Forums is what I tend to use - it's freeware with no ads, works on shared hosting, or proper hosting with the appropriate versions of php and mysql (If you're running a host that runs php 4.x, you need a new host anyway).
It has a really nice installer, an internal package management system for handling updates and plugins, with both official and additional repsitories and is nearly handsfree once you set it up initially.
SMF also allows openid logins (for 'social' logins) or there are third party social login plugins
It has entirely custom themes as an option and lots of layouts you can install through the package management systems.
I've been told it also handles better under large numbers of users than phpbb (I knew a guy who ran a large forum, and tried a few different things), but your mileage may vary.