4K
No, but seriously, your Photoshop/Gimp project should be at least twice as bigger as the final output.
If I were you, I'd compose everything in 4K, and then output all 4 scaled down versions (1920.png, 1280.png, 960.png, 480.png).
Let your app measure the user screen and decide the most appropriate size to use.
To minimize file size when using photoshop, do not use the regular "Save" function.
Use "Save for web" instead.