One more thought is that since the regulator on board is a linear it is best to keep the power to the DC in to 7.5V.. Less power wasted as heat. For best efficiency
(less power lost to heat) use a switcher to provide the power to the Uno DC in... Or provide direct +5V to the board from the same switcher... Either way will work. I use both methods... I have an Uno connected to a breadboard through a cable header and shield (From Liuder Via Inmojo)... The Uno is powered from the USB port and the breadboard has a linear board that plugs into the breadboard for the breadboard only and is powered by an external PSU. The grounds are of course common.
Doc