I'm not entirely sure which circles you are referring to. There are selection circles when you hover your cursor over a planet, or if you've selected it. Just move your cursor away and click in empty space to de-select. These also shouldn't show up when using the built-in screenshot and GIF tools. Certainly understandable that these may inadvertently get in the way when recording with other programs, though. We've talked about adding some sort of "cinema" mode, which would include more customization for what's included on screen.
You can already turn off labels by clicking View in the bottom bar. Click View > Show More (the 3 dots) for some additional options, and press Tab to hide the interface. Hope that helps!