Most people use APO/Peace (need them both) for EQing their headphones. The software is free and pretty easy to use. You can run a search for Hyper X Cloud Orbit S EQ profile and see if someone has already created something useful as a baseline or just start tinkering to see what sounds best to you.
Definitely plug them directly into your soundcard from the back of the PC using the 3.5mm connector. I don’t know much about this headset but I doubt that you would need an amplifier unless you are trying to add a large bass shelf via EQ. If so, you probably wouldn’t need much more than a Schiit Fulla or Schiit Hel+ which are both DAC/Amp combos (DAC = external soundcard). You would then just run a USB from the mobo to the Fulla/Hel+ and then connect the headphones to the Fulla/Hel+. You would also need a 3.5mm to 1/4 adapter because the headphone jacks on both of these DAC/Amps is 1/4.
Modhouse T50RP MkIII Argons can be ordered (although there is a lead time) for under $500.
Dan Clark Audio Aeon 2 Noire (with EQ) scratches my itch.
EMU Teaks have great slam but don’t extend as low into the sub-bass as the planars mentioned above.
I’m still trying to decide what’s next on my basshead journey. I’m leaning towards the LCD-XC because EQ is not a problem and I’ve worn motorcycle helmets 3x as heavy so their weight shouldn’t be an issue but always interested to hear what people recommend.