3-12V DC 12W Power Supply 7DC Plugs and USB Outlet | Jaycar Electronics
The power supply is expensive but you get what you pay for. The cheap ones aren't worth the risk.
This is probably your cheapest and easiest option. After you revise your code, you can upload it, disconnect the USB, then power the board with the power supply and the project should work just fine.
Alternatively you can use a servo shield for your Uno.