Maybe check out the modular synth community? It's kinda DYI.

EDIT: just noticed the analog there, I don't know anything about that.

As much as I would love to have a huge modular rack in my house, I am happy with a blend of physical and digital stuff. My first purchase was an Arturia Microbrute, which is just excellent for learning basic, monophonic synthesis. It's a knob-per-function device so there's nothing better than just twisting knobs and stumbling onto an amazing sound.

I send that through a cheap echo-delay pedal, then a reverb pedal, so I have a lot of control over the dynamics of whatever sound I'm making. I tend to use the Brute for basslines but it's super versatile.

From there, it depends on what I'm trying to make or play with, but I've had a great time using the Brute as both sound and MIDI input to get some nice layered input. VSTs are totally preferential of course, but I have the Arturia Jupiter 8 VST for when I want to get REALLY deep into analog synths without spending $25k on a working physical model.

Otherwise, I also have an Arturia Beatstep Pro (I'm an Arturia fanboi for sure, but their stuff is affordable and fun) which I can control the Brute with via CV in case I want to have it play a loop while I twist some knobs. I also have a profile set up in Ableton that allows me to use all the Beatstep Pro knobs to control various knobs/sliders on the Jupiter 8 VST, which has opened me up for a lot of possibilities. Beyond that, the Brute has a "mod panel" which allows for some fun stuff like jumping the LFO to the sub bass knob - the Brute is monophonic but has an overtone generator you can tune anywhere from -8 to +5.

It sounds like modular or custom synthesis are what you are looking for, but for my level of skill/time/hobby it's nice to have a setup that can fit entirely on an old Yamaha keyboard :)

The concepts are still the same, fundamentally. Unless you want to actually understand how to BUILD a synth and not how to USE one.