If you're interested in starting up a forum, you should look into how much you're willing to spend.
A domain name is pretty cheap to buy, but you'd have to have a host (which you can purchase pretty cheap) and a software. You'd have to be at least a little tech savvy to do this.
For free forums, I'd suggest:
MyBB Forum Software - It has extensions and plugins that you can use and it's completely free.
phpBB Forum Software - Again, completely free and has extensions and plugins. Has an alert system but not very social-friendly.
Jcink Forums - Hosting and forum software in one, very easy to manage and easy to navigate the admin cp and the moderator cp. However, it only allows adult content if you purchase adult content, which is a monthly subscription.
Proboards Forums - Hosting and forum software in one, I personally dislike it so I can't tell you much about the admin cp or mod cp. However, it doesn't allow adult content. It is strictly PG-13.
There's also:
Xenforo - This is what is used here, however you have to purchase it.
SMF - I don't know much about this, but I do know that you have to buy it I believe.