Connecting an Xbox One controller via Bluetooth is not supported on Windows 7:https://support.xbox.com/en-US/xbox-on-windows/accessories/xbox-one-wireless-controller-differences-on-windows-operating-systems
Anyway, vibration doesn't work perfectly via Bluetooth, so I recommend that you buy an Xbox Wireless Adapter. Note that there are two versions of it, and only one of them supports Windows versions other than 10.https://www.xbox.com/en-US/xbox-one/accessories/controllers/windows-wireless-adapterhttps://www.xbox.com/en-US/xbox-one/accessories/adapters/wireless-adapter-windows
The Steam Controller is also a good choice if you don't mind having to get used to it, and to fine-tune its configuration for every game. Once you do, it has the advantage of a very good motion sensor, which is really helpful for shooters. And it allows you to wirelessly control your entire PC via its keyboard and mouse emulation.