Thank you all for your answers! I know what to do now 
I’ll buy a 12V AC power supply and buy/build a ±12V rectifier then. The Microbus Frequency Central seems like a good, simple and reliable option but I might end up trying to build one too.
For all newbies like me: I stumbled upon a video on Youtube that explains how this circuit works, in a clear and simple way: https://www.youtube.com/watch?v=pQKN30Mzi2g
I’m not saying this is the best way to understand this, but it helped me a lot.
Note: you might want to watch this other video first: https://www.youtube.com/watch?v=QBatvo8bCa4 which explains the function of basic components such as resistance, capacitors, diodes, etc.
By the way, I saw this other topic Opinion: Don't try to add stuff to a Super Simple Oscillator - #6 by analogoutput and yeah, I’ll probably end up building a more sophisticated oscillator – it’ll be simpler than the SSO in the end. Still, the SSO sounds really good and I’m really having fun with it – here’s some random noodling: https://www.youtube.com/watch?v=xZq0geQHRR4