There's two Joomla! extensions called JoomSuite Member and JoomSuite User that you want to get to set up permissions to your membership site and set up subscriptions. Subscriptions allow you to control what users get access to and give you the ability to set up payments for membership. They have integrations to most of the major payment gateways like PayPal and 2Checkout. They also handle recurring payments with ease. It's an inexpensive solution for membership on Joomla!.

The JoomSuite Member package is $99/Year and worth every penny.

You may see the Joomla! extension called Community Builder CB, but I suggest holding off installing it until the releases are stable. You should see that in the next few weeks but for now it's kind of buggy and unless you're a programmer who knows PHP and MySQL and you know you're way around Joomla! it will be over your head.