Most painless way to put the UI onto a predefined 2D space?

I want to put Unity's UI widgets into a predefined 2D space on the screen. Place them on-top of a sprite basically. So not the relative default system where the rect gets calculated by the system.

I am well aware, that I need to set the Render Mode of the canvas to Screen Space, but positioning is awkward. The predefined button appears as a large blob this way, and resizing/rescaling produces funny results.

I think am missing something. What is it? Anyone here who knows a good tutorial for this use-case?