If not actually needing that mic, forget word headset and go for headphones.
There are good headphones from actual audio makers for slightly over £100 level.
Like Beyerdynamic DT770 and DT990 depending on do you have noisier environment or quiet.
For sound card Creative Sound BlasterX G6 can be found at real good price from B-stock to keep total budget around that £200.
DT990 has good amount of bass punch for gaming immersion.
Though as open design it can't do lowest rumbling bass like closed headphones.
But anyway much more bass than that and it starts to seriously bury details in games if you want easily distinguishable foot steps etc.
Also Beyerdynamic's design would be easy to DIY mic mod:
https://imgur.com/gallery/bKU4H
SB X3 would have head shape customizable Super X-Fi HRTF as extra in addition to fixed average head shape based HRTF.
But as sound card X3 has rather mid level D/A converter (at level of Sound Blaster Z) and neither is headphone output much better.
(while SBX G6 has good enough headphone output for most headphones you could buy)
Though unless you're serious about retiring your hearing prematurely it's enough for DT990, which also has profile in Super X-fi to increase sound positioning accuracy.
SBX G6 is definitely superior in analog audio hardware quality.
But if you have head shape differing more from average, Super X-fi could improve sound positioning good amount.
Though SBX Pro Surround is definitely among the better fixed HRTFs.
There are some gameplay recordings in Youtube you could use to test if SBX Pro Surround works.
Like first couple minutes of this being excellent quick test for headphones:
https://www.youtube.com/watch?v=d1_20T8x_OI
If headphones are accurate, besides directionality there should be also feel of distances.
So could start from headphones.
Fashion "DACs" like Schiit lack features of sound cards like HRTF and you would be relying on game having HRTF or software.
Also mic inputs aren't that common making adding mic later more complicated, while mic input is standard feature of sound cards.
There are cheaply available 3.5mm microphone's with headset type flexible arm you could attach to DT990 and just use extension to connect it into sound cards.
GSXes are normally extremely brand hype overpriced for using cheap sound chip meant for cheap phones/tablets.
D/A conversion (that's what DAC actually means) is literally at level of Audigy Fx/Xonar DGX and it basically lacks proper headphone amplifier and would struggle with any harder to drive headphones.
(with that pricing per hardware quality SBX G6 would cost like £500)
SB X3 would be class up in hardware.
It's going to come down to personal taste.
FWIW I picked up a pair of DT770 Pros (80 ohms version) a week ago for my gaming laptop and comparing them with my wireless Corsair Void Pros they're night and day, and that's without an amp. I was explaining to a friend earlier, the Voids are ok (let down by the rubbish software) but I tend to get lost in the bass and general noise. With the DT770's everything is clear and crisp, bass isn't deafening to the detriment of all other sound and I'm finding it easier to pinpoint where exactly something is coming from - and my hearing isn't great (misspent youth going to gigs and standing directly by the loudspeakers!).
I love the build quality of the DT770s and I find them very comfy (the Voids are damned heavy as they're wireless).
Got mine from the Bolton boys with free delivery ordered on a Wednesday afternoon delivered next day around lunchtime.
I have the DT770 pro 250 ohm and I love them. They are not bassy the way most headphones are, however. Most bassy headphones seem to just rattle your skull but have very little or reduce detail in the low end. These do a bit less rattling but seem very precise and the sub base is eargasmic IMHO. They can seem a bit high pitch in the beginning to some people but it's never been something that has bothered me. They are incredibly detailed for the money and IMHO a good place to start if proper quality audio is something you are interested in. I'm in no way an expert in audio so take my statement with some salt but I do love me some quality audio.
The DT770 pros would fit you well then.. Nice clean sound with detailed bass and insane low-end performance. Try listening to ->this<- on your Astro's and when/if you get the dt770's and you have them powered properly then listen to it again. I'm sure you would be able to appreciate the difference.
MixAmp uses ancient Dolby headphone, whose bass bloat is pretty horrible for details with anything above neutral bass headphones.
(+ there's DH's tendency for lots of echo)
Creative's bass neutral HRTF is lot better and doesn't try to bury details.
And headphone output of SBX G6 is lot more capable.
At hearing safe SPL for long term listening sound leak from open headphone isn't really heard far away. (except in completely silent environment)
But without hearing dangerous SPL any sounds in room like TV would leak through easily.
So closed headphone is the only choise for that environment.
32 ohm version has leather pads.
80 ohm and 250 ohm versions have velour pads.
For gaming and movies you'll want to have headphones and 7.1 chosen.
That makes Windows and games think you have 7.1 speaker set and sources supporting more than stereo channels output surround sound.
Then sound card can continue from that using HRTF algorithm when having surround enabled.
Different filters shouldn't have much any hearable effect.
You could try playing back some music with full range of frequencies to find if there's difference.
Minimum phase filters could affect sound positioning by basically delaying higher frequencies compared to lower frequencies of impulse.
So could start from Fast Roll off - Linear Phase.
This could be used as material for trying to listen if it affects gaming:
https://www.youtube.com/watch?v=d1_20T8x_OI
(disable surround to let signal through as unprocessed stereo)
ModMic is that easy to use solution if you want headset style mic.
But looking around for "3.5mm detachable microphone" would give some options for doing that cheaper DIY modding.
https://imgur.com/gallery/bKU4H