Idea:
Create a sketch on my computer, load it to Arduino Uno.
Check if it works
If it works, I want to unplug the USB, walk to my (indoor garden) and run the sketch on the Arduino without being connected to the USB.
(and maybe be connected to Wifi, via a shield; but that is second part of question)
No need to connect the external power supply in parallel with the USB
Once the code is uploaded to the Uno it will not forget it. The code will run whenever power is supplied to the Uno so you can
1 Connect the Uno to the PC via USB
2 Upload and test the program
3 Disconnect from USB (Uno will power down)
4 Move Uno to required location
5 Connect external power to Uno (Uno will boot and run the code)
6 Repeat step 5 as often as required
An easy way to power an Arduino away from a PC is with a USB charger and USB cable.
If you are getting a plug-in power pack to connect to the Arduino's power jack, 7V is the best voltage. Higher voltages just mean that more power is turned into heat in the voltage regulator on the Arduino.