
Sennheiser
HD 560S
Budget gaming king with clear sound, but tight fit.

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It depends on which model you got. The DT 990s come in a range of impedance levels- if you got the 80 ohm version or the Pro X model (48 ohm), chances are your motherboard really is enough to power them and buying an amp would have minimal benefits. If you're happy with the sound, don't go out of your way to spend more money on them.
I don't have a DAC myself but I believe Fiio's are meant to be good value. Again though if you're happy with the sound you're happy with it.
My brother has DT 990 Pro X and they need to be EQ’d however this is really simple and you can find everything really quick with a couple searches. I’d never done anything like it and set them up in 10 mins for him. They are insanely good i unfortunately am not a headphone user but I tested them out on valorant for a short period and the pin point accuracy of footsteps on and being able to time someone walking round corners because of the accuracy of the imaging. This was something that made me dive into the audio space because I couldn’t believe I’d not invested in decent audio before.
They definitely need EQing. straight out the box they weren’t great but very easy fix. I suppose it depends what you are looking for. You mentioned gaming so I assumed you wanted that wallhack type of sound.
X2HR has to be the worst headset I have owned for gaming. While the soundstage is good, telling where people or sound was coming from was very hard, horrible imaging. They also had an uncomfortable spiking treble for me. I have 12 headsets now, ranging from open to closed back, dynamic and planar drivers, so i have a good range of headphone to compare against even the X2HR is sold now. At this price range, the Beyerdynamic DT 900 Pro X would be a superior headphone for gaming, or the FiiO FT1 Pro if OP wants open back. For Sennheiser there is maybe only one headphone that is truly great for gaming that is close to OP's price range (but probably too expensive) and open back, and that is the HD 490 Pro. The other Sennheiser alternative is the 560s
If OP want to hear the surroundings, the open back Beyers would be better, like the 900 Pro X, or the 990 Pro X.
Stop here. Don't buy anything else. Pro X doesn't need an amp if you're happy with how loud it gets. This is the one and only "wow" feeling you'll get, everything else is chasing this feeling again and you eventually end up with $5k headphones. Amazing gear, happy you're happy.
I went through the exact same process you’re going through about 2 weeks ago. After some research I went with the beyerdynamic DT 990 pro x (open back). Crazy how much better the directional audio is compared to the Arctis Pros I’d been using for the past 8 years. Funny enough Arc raiders is also the game I’ve been playing and the reason I made the switch was because I was having trouble figuring out where sounds were coming from. The improvement in audio detail was mind blowing.
1990 MK2 is great, 990 Pro X treble is HORRIBLE for games. join the HD 490 gang.

Sennheiser
HD 560S
Budget gaming king with clear sound, but tight fit.

Sony
WH-1000XM4
ANC king, durable, but unreliable mic and touch controls.

Sennheiser
HD 6XX
Legendary mids, durable, but narrow soundstage and weak bass.

Sennheiser
HD 490 PRO
Super comfortable, wide soundstage for gaming, versatile pads.

Sennheiser
HD 599
Super comfortable, easy to drive, wide soundstage, open-back.

Ranked #1
Sennheiser - HD 6XX

Ranked #1
FiiO - FT1 Closed-back Headphones

Ranked #1
Sennheiser - HD 560S

Ranked #1
Sony - MDR-7506

Ranked #1
Sony - WH-1000XM4

Ranked #1
Sennheiser - HD 560S