Zetaboards, definitely. I've been with Zetaboards since its opening in 2007 and I'm just so used to it. But I'm pretty sure it's beginner-friendly as the Admin CP is straightforward and the post buttons aren't small. (*cough* Xenforo *cough*)
Doesn't ZetaBoards use Invision Power Board? I would never use a hosted forum service like that, I like being in control of my data.
I initially started off using SMF but disliked the admin panel a lot and the way that you had to install plugins. Then I switched over to MyBB and have yet to be disappointed. I like the overall feel, user-side and admin-side.
In my opinion, phpBB. Because of its advanced features, and customization. I can easily make a custom phpBB style out of this. But in my opinion, I wouldn't start out with phpBB since its more of a "advanced" forum software.
I personally like Xenforo's forum software when it comes to design and features. I can accurately view my posts accordingly to the interval of time when I posted it. Unlike with others where my newest post don't appear as soon as I posted them. I also like the alerts feature there wherein I can see who quoted, replied, and liked my posts.
I think Xenforo is the best software right now. I tried out their test board and I really like it. I do think it has potential to eventually get bigger than VB. For the free ones, I think it would be mybb. It has come a long distance since the beginning.
IP.Board is hands-down the cleanest, most powerful forum software in my opinion, alongside vBulletin. Both are so integration-capable, there's almost nothing you can't do. IP.Board 3.2.1 just came out, take a look at it on invisionpower.com. It's very attractive and has social media integration pre-loaded.
vBulletin is the most powerful but MyBB is not bad i prefer using it
"I prefer using MyBB, because it looks more professional than the other free forum softwares. I only will ever purchase a license to a paid software if the community gets big enough and I think I need it. Besides the point, MyBB has a great and easy interface, for not only users, but the moderators and administrators too. It has plenty of modifications to choose from, a great wiki, plenty of settings, and it always has amazing themes, which are quite easy to code yourself."
VBulletin is unbeaten by anything and is by far the most feature filled and most convenient. XenForo is pretty good as well but not quite as good as VBulletin.
phpBB is horrible and MyBB is not a whole lot better.