Dude for a first setup any of the $200 entry-level stacks would be great choices, JDS Labs Atom Amp + Atom DAC, Magni 3 + Modi, etc. For gaming the Beyerdynamic are hard to beat at this price range. 770, 880, 990 are all top-notch gaming cans. I would say 770 for more “fun” gaming and 880/990 for competitive. The Sennheisers (6XX, 58X) are good music listening headphones but I find them fairly lacking in gaming performance. They just lack the imaging and soundstage width for dimension and positioning.
Now for music, I think that will depend on how much treble you like. They can be fairly harsh if the music is recorded poorly. However, I still think the 880 and 990 sound fantastic when the music isn’t shit recording and mastering quality. I think the 770 80ohm version is a better choice for portable because the iPhone dongle cant really power the 250ohm versions of the 880 and 990. I’ve seen others mention the 177x GO and I would also recommend that. It’s going to have a less harsh signature than the lower end models, way easier to drive so more portable, closed-back for isolation, and a removable cable. It’s a lot more expensive but definitely worth considering.
The sound leak on the 880 and 990 is not actually that bad and if you’re in a room by yourself no one would be able to hear it.
Any $200 AMP+DAC stack ----> 6XX,58x great allrounders for music and ok for gaming.
Any $200 AMP+DAC stack ----> 990, good for music might be harsh, fantastic for gaming
Any $200 AMP+DAC stack ---->880, not as good at mainstream music because of less bass but amazing for orchestral and acoustic stuff, fantastic for gaming.
Any $200 AMP+DAC stack ---->770 80ohm, good for music, vocals will seem recessed comparatively, Bass + good soundstage for closed back makes for incredible singleplayer gaming experience.
Any $200 AMP+DAC stack ----> 177x, great allrounder for music, fantastic for gaming