switches - Signal path switching for effect circuits

I'm trying to build a method of switching signal order with three circuits in a rack unit.

I've been researching different methods, using relays, using CMOS etc but I'm getting a bit overwhelmed and lost. I don't have a lot of technical experience with electronics apart from building kits and using an Arduino every now and then.

Say circuits are A, B and C; I would like to order them ABC, CAB, BAC, ACB.

Could anyone point me in the right direction on this? Any recommended reading on CMOS or even a chip recommendation?

Thanks for reading!

Edit: Added a picture to make it clearer, all signals are analog (line-level).

Answer

This will be a continuation of Trevor's answer. So the design will be fairly similar.

I'm not sure how much you like relays, but I prefer transistors to do their job (whenever possible). Because of the physical size, price and energy consumption.

I'm using two N-MOSFETS as a transmission gate, but in order to properly open them and close them you will most likely need 12 V and -12 V, those can easily be made with a charge pump and an oscillator.

I hate seeing negative voltages at the top of the schematic, but since the Falstad Circuit JS doesn't support proper wire dragging I decided that it was not worth my time. Had this been something job related then I'd redesign it with -12 V at bottom and 12 V at the top. I realized my wrong doing very late at the design stage.

Here's the text if you want to interact with the button at the bottom.

If you want to simulate, press the Circuit JS link, when you are at Circuit JS, click file at the upper left. Choose "file > import from text" and copy and paste the text from the text link. This is the first time I've made a schematic with an URL that's too long. Oh well.

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EDIT: Realized you don't need the PMOS at the bottom if you connect your switch to 12 V instead of 0 V.

So it should look more like this:

If you look at the output, I changed the pull down resistors so they are correct.

This is the design I'd solder onto a PCB and be happy with. But I'm no audiophile, I can't even tell if someone sings bad or not. Music ain't my thang.

Here's the text for this circuit if you want to test it out.