This is going to sound like an ad, so let me just say this: I am in no way affiliated with SMF.
Simple Machines Forum is pretty awesome. It's what's running here and I've administered several installations of it in the past. Pretty simple to set up yourself, and the package manager allows you to easily customize your forum with modifications to create your own unique experience, all without touching a single line of the PHP it's all built in. Along with mods, a massive library of themes exist to visually differentiate your community. Alternatively, you can duplicate the default one and modify it to match your site.
Now, I don't know much about Wordpress, but there's probably some kind of module or plugin for it that can interface with SMF. If not, you can probably build your own on top of SMF's included SSI library. The library itself is written in PHP, but as I understand it, you can elect to access it with HTML using server-side includes. The syntax for that looks a bit funky to me, but that's probably because I'm just used to using PHP for all my server-side scripting.
If you don't know PHP, but wanna learn, the online documentation at
PHP.net is thorough. For starting out or a quick basic reference, though,
W3Schools has a section on PHP. If you use Chrome, a really good extension to install is
PHP Ninja Manual, which is very handy for quickly searching the PHP.net docs for things like function syntax.
If you go with SMF for your forum software, I'm also available to help out there and could probably write some code to get Wordpress to pull information through the SSI library if necessary. But, like I said, there might be a plugin or whatever for that already.