Joomla currently doesn't really have a good way to distinguish between "regular" website users and premium (paying) members, because it has a rigid user group structure (this is set to change with the next version, though - of course, in true Open Source spirit, that will be "ready when it's ready"). There are extensions available that add this kind of thing onto the base system, though, like JUGA. For phpBB, there is a very nice bridge available in the form of the Rokbridge, although that does not offer template integration (so you'll have to put in some elbow grease if you e.g. want to replicate your sites menu structure on the forums).
I am personally very much in the same situation (also a national car club, be it in the Netherlands), although my current site is custom coded, except for the forums, which is phpBB. I am currently working on a new site based on Drupal, which at its core is more suited for community sites. I am planning to continue using phpBB for the forums, because that's what I am using now and the impression I have of the Drupal forums solution is that it is not as fully featured as phpBB (building a system completely based on Drupal - or at least analyzing what's missing - that can match phpBB feature for feature may be a next project
The only challenge I have is that I am not particularly thrilled with the current options to integrate Drupal and phpBB, so I am working on my own. On the one hand, I'm a bit bummed that I'm not using any of the available offerings (not at all the Open Source spirit), on the other hand neither of the two options are particularly mature. I may end up posting my solution on Drupal.org when it is finished.