You can have a normal ap acting as ap client and getting the internet connection from a wifi router. I had it this way and performed quite well. As for the security issues, you can use whatever security encryption you want, it's only for the ap-router connection, the mini would get the connection via ethernet.
You don't have to set a bridge, only need your router set up normally and wifi active, then, with the ap(that it would be to the mac mini) configure it as ap client, and from there, connect an ethernet cable to the mini. Essentially the ap is acting as a wifi card, the difference is that instead of using a usb port, or the internal airport, you are using your ethernet port.
I had this until my ap died from some strange reason. Now i'm using a pc with debian acting as router, but soon will get another ap to get it directly the connection as it had originally.
Cheers!
