Mac networking.

I have a PC as the host of my lan. It has a Belkin router, so when I hook up my Mini will Airport catch onto the routers signal? I have no clue how Airport and Mac networks go. All I know my Mini comes with Airport and Bluetooth 2.0

Yep.
Airport is just apple's name for wireless lan... If your router has wireless access enabled, the mac will pick up the signal and join the network. (You might need to enter the password for your network if you've enabled encrpytion).

Ah, good. Yeah we have it encrypted.