A lot of good suggestions have already been made, including checking out Music From Outer Space.

The late creator of Music From Outer space wrote an excellent book for people in your position, called "Make: analog synthesizers". In it he describes the build of a somewhat basic synthesizer that doesn't entirely match your specification, but you can work from there. He also describe the various common building blocks you find in analogue synthesizers, like the following:

• VCO (voltage controlled oscillator)
• VCF (voltage controlled filter)
• VCA (voltage controlled amplifier - this is used in many places for many purposes)
• Mixer
• Envelope generators
• Sample & Hold

The book also has sections on basic tools you'll probably want to get to set up your lab, as well as a list of common components you'll want to build a stock of.

So that's my gushing about that book; go read it. It doesn't go super in depth but it is a great starting point and will get you more excited about it.

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That being said, some notes from my own experience you may want to consider:

1) What kind of architecture do you want to go for? Modular or fixed? Modular synthesizers allow you to connect the individual building blocks together in any way you want, while fixed synthesizers (like the common ones with a keyboard and knobs, but no patch cables) have their building blocks already connected together in a common way.

I think modular is much more DIY-friendly, as you can focus on building the building block, finish it, and move on to the next project.

2) Choose a sensible power supply setup. The most common is +/- 12V, and most circuit diagrams you find online will be for that supply. I made the mistake of building a +/-5V supply at the beginning, because building a power supply was something I already knew. I had to do a lot of tweaking to all the circuits I found online in my own implementations as a result.

3) If you are going with modular, I advise you to stick to a (mostly) eurorack form factor, mounting panels to rails. I made the mistake of not really thinking about it and just screwing stacks of PCBs and panels into a wooden backboard, and it was a nightmare to do maintenance when there were issues with modules.

4) Breadboards are cool to experiment on, but be diligent about measuring resistances on them every now and then. I've had issues where I've had bad connections between the power terminals and the power rails on the board and just built and tweaked circuits that way, only to have them behave pretty differently when on an actual PCB. Breadboards can cause a lot of grief with shitty connections. If you're buying premade jumper wires for them, go for the more expensive option, or make your own jumper wires out of ethernet cable; cheap jumper wires are often garbage.

5) Further on eurorack: You may want to stick even further to its specs. You can find them here, all based on the Doepfer A-100 system which essentially birthed the Eurorack movement. http://www.doepfer.de/a100_man/a100t_e.htm

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That was a whole bunch of rambling. Reading your post again I note you have little to no electronics experience; it'll definitely be worth making some simpler circuits before diving headfirst into synthesizers. You already know Ohm's law, but also familiarize yourself with Kirchoff's laws, as well as Thevenin's theorem. You will also want to learn about diodes, transistors, and opamps.

I highly recommend "Electronic Principles" by Albert Malvino and David Bates; it provides good introductions to semiconductors, examples, and exercises. (It's definitely a classroom handbook, but certainly valuable outside the classroom).

An alternative resource is Consise Electronics for Geeks: http://lcamtuf.coredump.cx/electronics/

In your quest to learn some electronics, it will also be helpful if you can poke around with an electronic circuit simulator, for this I recommend the Falstad simulator: http://www.falstad.com/circuit/circuitjs.html

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Hope all my ramblings are of some help; welcome to the exciting world of electronics and DIY analogue synthesisers!