Whatever you do, keep the forum separate from the game server. Hosting a PHP forum that's written without sql prepared statements is a sure way to get your entire LAMP stack hacked. All those forums are security holes with functionality on top. Oh, and don't even consider SMF. I've seen the code, I'm not the man I used to be...
Yeah, the forums are hosted in a completely separate DB server, but i'll still need read access to the AuthDB so I can perform login authentication.
Simple Machines looks like a Simple Nightmare..

I ended up purchasing XenForo due to many reviews favouring it and to me a price of $140 USD for indefinite use, a year of support and a cheap renewal fee per year if I want updates seems very reasonable.
I didn't want to go with a free solution because afaik paid solutions will and usually do patch up their holes quicker, have less security issues etc.
I was disgusted by the code in vBulletin 5, and I really despise the code in MyBB (downloaded latest one to take a look, doing evals to output templates..?). Didn't even want to check PhpBB out because I thought it was just extremely ugly.
To me, XenForo is clean, it's extensible, and just looking at the directory structure I can say that it's organized extremely well.
I guess we'll just need to see where this goes.

Thank you all for your replies!