Any Wired 360 controller should be pretty much plug-and-play on Win7, though you may need to get the drivers from the Microsoft website. Any game that supports gamepad/joystick control should work with it, more so if the game allows for key remapping. The Wireless controllers however require the wireless receiver, which MS stopped making some time ago, though you can find third party ones on eBay, I have not tried either version personally. Some have claimed to get the wireless to work through the play and charge kit, however I have never seen any proof of this working (I have tried with several controllers and several P&C cables with no success.)
The original Xbox controller would need an adapter to convert it to USB. You might still be able to find them online if needed, or if you can solder, you can splice one at home.