So after some research I found a way to use both a wireless Xbox 360 controller as well as a wired third-party Xbox 360 controller. This worked for Borderlands 2 and other games I've tried so far. The cost for this is $5 for the wired controller and $20 for the wireless. Here are the two setups that worked for me.
Step 1: Wireless Xbox 360 controller
The computer still wasn't recognizing it, so I installed Tattiebogle 0.11 which you can download here. Follow the instructions for installing and then open up the "Xbox 360 Controllers" icon in your System Preferences.
Link up your controller to the receiver and you should now be able to see reactions to you messing around with buttons and analogs on the 360 controller.
This is great, but many games will still not recognize your controller. So now you need to map your buttons to keyboard commands. To do that you will need to get Joystick Mapper in the App Store.
Once you're in Joystick Mapper you can assign all of the buttons and analogs to keyboard and mouse controls. This will take some trial and error to find out what works best for you, but it does work.