Look in to FM synths, same way that SOPHIE gets his bubbly sounding sounds and such. It's a bit (a lot) more abstract than additive synths so if you are new then maybe learn first by playing with sine waves in additive synths and then move on to FM, but if you are dedicated you can learn FM synthesis as a first time thing. I like FM8 by Native Instruments.
I'd recommend the KORG M1 Legacy VST as a good place to start for sample based production. It's an emulation of the old KORG M1 workstation which, from a music production standpoint, is kind of iconic towards late-80's/early-90's culture. You can hear this particular VST, or at least sample sets very reminiscent of it, being used in a lot of PC Music works. For instances of M1 usage, listen to some of the earlier A.G. Cook stuff. Danny L Harle might also be a fond user, 'Aquarius', for example, screams M1.
If you're feeling brave, for a more clinical and refined approach to the PC Music sound you might want to try FM Synthesis. FM8 is probably going to be your best friend here. FM Synthesis, or at least the use FM based samples, are pretty prevalent throughout the PC Music catalogue. The sounds resulting of this kind of synthesis tend to be considered somewhat 'artificial' and 'digital', which is why I guess it ties in so well to the whole PC Music aesthetic. Beginners, though, might want to steer clear of FM Synthesis until they have a better grasp of fundamental acoustic principles, picking up a complex piece of software like FM8 can be a pretty daunting task for unfamiliar users. However, if you can wrap your head around it, it's infinitely rewarding. For examples of FM Synthesis I'd suggest listening to pretty much any of SOPHIE's work. I'd be pretty confident to gamble that at least 80% of his sound design work is done through FM synthesis alone, with the other 20% left to something I can't quite put my finger on (maybe granular synthesis?).
For the sounds you're referring to in particular, just look for supersaw based sounds. Most synths are capable of these sounds. Just stack a few saw waves, turn up the unison and detune, and play some big chords.
SOPHIE also uses the Elektron Monomachine for his production. It's the only physical synth he says he owns. Here's a link to an interview he did with the company that makes the Monomachine. There's some insight into how he works such as only using the Monomachine and software. It's an interesting read even if you're not into synthesizers and such.
Does anyone have any good ways to learn fm synthesis? Everything I find is pretty poorly done and not explained well. I understand the idea behind it but I don't really understand the controls work. And any free fm synths for logic would help because right now I can only use the half hour demo for fm8.
Also, I'm guessing the korg m1 synth is not FM synthisis? What would it be considered? How would I got about learning how to use it?
Thanks for the awesome history lesson! I really love that plastic-y sound. So iconic. There is a quote that I think applies to what you are talking about and pc music in general.
“We are nostalgists as much as we are futurists. We blissfully relive the 8-bit primitivism of a bygone age, preserved forever by the endless archival capacity of the internet, whilst utilising those same networks to shape the fantastical landscapes of tomorrow. […] We are thus cynics, and yet eternal optimists, our technologies driving our melancholia and invention in equal measure.”