A used DSLR is pretty much what I had in mind, or a used mirrorless camera, if there are any advantages of those over DSLR, aside from (perhaps) the price.
When it comes to different lenses for different types of sensors, I assume that different camera manufacturers use different standards for mounting the lenses, and that for the same manufacturers, it again depends on the sensor format (full frame, APS-C, 4/3rds), right?
Vibration reduction is the same thing as image stabilisation, right? I think I'd agree there, my requirement for mobile phone cameras is that they have OIS built it, as I do have a slight tremor, and carrying a real tripod seems really impractical.
About tutorials and guidance, I'm mostly wondering how do I recognize a good deal on a camera, and what to search for, as well as some explanation what does what (e.g. what ISO settings actually do). I found some tutorials on YouTube already, so I'm searching for some channels that do it the fun way, preferably aimed at someone who doesn't have much knowledge of the camera market or who is rather willing to buy a used camera than a brand new one.
That being said, I'll take
@Matt2000's tip and play with my phone's manual settings, and generally play around with my phone's camera. Now, my dad could be a bit of help there, as he did even some semi-professional photography back in the pre-digital days, but he generally tends to go into long explanations and doesn't do very beginner-friendly explanations. In short, he pretty much involuntarily sucks the fun out of it. But I guess if I get some background through e.g. tutorials, I could make use of his tips.