You probably won't get something worthwhile for that money, alas. If you can get a secondhand behringer recreation of a classic synth at the right money, you might be close.
I've taught music technology for over 20 years, and getting a simple subtractive synth and playing with it is the best way to learn this kind of thing. The temptation is always to get something vast and massively complex (as the presets will sound amazing), but in terms of learning how to actually program a synth, a basic one is way better. Something like the Roland SH-101 (which behringer have made a copy of) will let you understand all the elements of it that you can then translate to the complex structures of larger synths.
I find cherry audio's voltage modular a great learning tool, if you take the right (basics first) approach - as it can get very complex very quickly otherwise!
If you're going with software eurorack emulations as a didactic tool, VCV rack should be pointed out, too. The standalone version is open source: https://vcvrack.com
The basic modules that are included let you form the core of subtractive synthesis. Having them available as isolated, wired up building blocks is a very visual help in understanding how they relate.
I've taught music technology for over 20 years, and getting a simple subtractive synth and playing with it is the best way to learn this kind of thing. The temptation is always to get something vast and massively complex (as the presets will sound amazing), but in terms of learning how to actually program a synth, a basic one is way better. Something like the Roland SH-101 (which behringer have made a copy of) will let you understand all the elements of it that you can then translate to the complex structures of larger synths.
I find cherry audio's voltage modular a great learning tool, if you take the right (basics first) approach - as it can get very complex very quickly otherwise!