I want to approach this type of minimalistic motion graphics, where do I start for this specific style?
The best choice will be to play with Animation Nodes and use to different objects with geometry of circle and ico-sphere for the shapes and a small sphere for the balls.
And then using the proper nodes change the position of the instanced spheres to the between the vertices of ico-sphere and circle.
Here, I mean you should have same number of vertices on both the circle and ico-sphere. And then use a mix-vectors node to change from circle positions to ico-sphere positions and back. Here's some documentation: http://animation-nodes-manual.readthedocs.io/en/latest/user_guide/nodes/vector/mix_vectors.html
Here is something I created,
And only thing to keep in mind is that you must have same number of vertices or it might look weird and might not work either.
Also remember to turn on motion blur which I seem to have forgotten.