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The Stern-Gerlach experiment is imo the best way to learn the basic idea of quantum mechanics as derived from a reasonably simple experiment. Much better than the double-slit experiment which is more confusing and about which there is a lot of terribly incorrect discussion online.

I would recommend another source with some nice diagrams though, like hyperphysics, or the opening chapter of Modern Quantum Mechanics by Sakurai (although it's a graduate level book, the opening chapter is simple enough).

Yeah, I would not point somebody unfamiliar with Stern-Gerlach trying to learn "the basic idea of quantum mechanics" at Sakurai. Feynman lectures vol. 3 maybe
Here's a 26 minute lecture walking through the construction and operating principle of a Stern-Gerlach device and demonstrating it's use. I recommend at least watching a measurement towards the end, but honestly the whole video is amazing.

The Stern-Gerlach Experiment (ESI College Physics Film Program 1967)

https://www.youtube.com/watch?v=AcTqcyv-V1I

I still dont grasp what a spin of an electron is. The image of a spinning sphere doesnt help - as if you can roll this sphere you will see there is no different spin - it has only one spin direction and you cant differ two spheres apart by its spin. Even worse if I would consider a point - how should it spin as it is the same in every direction of the space. As it is described by mathematical spinors (tensor) I still would like to see an equivalent in my sphere of experience to grasp it completely. (spin plus minus 1/2). Odd enough the spin can combine and couple with the angular momentum it feels like the spin should be something that ought be visualised.
don't imagine a ball spinning. Imagine a spinning top. It acts as a gyroscope. When a force is applied to it it tries to resist it, but it also causes precession. The equations for that precession can be used for electrons in a particular context. This is how we discovered that particles have angular momentum in the first place. Whatever we measure in that context, is what we call a particle's spin. It's all about the angular momentum and the precession caused by an external force.

tldr: nothing is spinning in a particle. what we refer to as spin refers to how angular momentum is affected by external forces, which happens to behave similarly to a spinning gyroscope. So we called that property "spin"