I don't know if shooting on Auto will help learn though.
Frankly I shoot horribly on Auto, and that is since I ditched my last fixed focus film camera (means has nothing to do with using SLRs), and consequently have a hard time with smartphones and elph cameras.
Fast movement- go with Tv, auto ISO, auto WB at least. Try to shoot RAW if possible, or both- then you get flexibility of tweaking and practicing with some of the images while not holding up the pipeline.
My humble 2c.
That depends on experience. It's never best to learn everything at once, as a teenager I used an Olympus XA/2 which is fully automatic except for a choice of three focus settings (head and shoulders, full portrait, landscape). That allowed me to concentrate on the framing before moving on to my first SLR.
By the time I had my OM-10 I was thinking about composition and framing automatically, and started to experiment with aperture and focus. Everything else was automatic, it's an aperture priority camera. I did, when I was ready add a manual adaptor, so that I could push the boundaries further.
My point is that full auto may well be a good place to start, to get a feel for the camera. Then the semi automatic aperture and shutter priority modes, leading to full manual. Just don't get distracted by the scene modes. It's a journey.