The classic Forrest Mims books are a good start: https://archive.org/details/electronics_-_Forrest_Mims-engineers_mini-notebook_555_timer_circuits_radio_sha/page/n1 -- see the Toy Organ and Stepped Tone Generator entries

He also had a intro to the basics book: https://archive.org/details/Forrest_Mims-Engineers_Mini-Notebook_Formulas_Tables_Basic_Circuits_Radio_Shack/page/n1

The 386 op amp here is pretty basic: https://archive.org/details/Forrest_Mims-Engineers_Mini-Notebook_Op_Amp_Ic_Circuits_Radio_Shack_Electronics/page/n5

(you can find a lot of online tutorials for making a simple 386 audio amp, though)

The Mims books are classics because they are pretty easy to understand, but at the very least they might get you started so you have a better idea of what to search for. But for something like a 555 oscillator or 386 amp you pretty much just need a breadboard, some wires, a couple resistors and capacitors, and a speaker for the output. The speaker will just connect black to ground and red to the output pin on the circuit.

Here's something I built with a 555 timer: https://www.youtube.com/watch?v=tjceNARrR4w -- the knobs control resistance and the buttons activate capacitors, which alter the pitch depending on the size/rating of the capacitor.

This isn't synth-related, but this is a small 386-based (and Arduino-based) guitar amp I made: https://www.youtube.com/watch?v=9FoRHpJfV2Q -- I kind of cheated with the op amp and used a premade module: https://www.amazon.com/gp/product/B01FDD3FYQ -- although I've also made my own LM386 circuits as well.

BTW, I'm a big fan of Elegoo and their various kits. I've been happy with the quality and with their customer service so far.

​