Any "surround" or word like that in headphone box basically means content is big pile of trinket garbage.
Good (non-fashion/gaming garbage) stereo headphones is all what's needed.
We hear in 3D because shape of the head causes direction dependant changes/differences to signal received from sound source by both ears.
Brain simply calculates location of sound source from those timing/amplitude/frequency response differences.
In real world those binaural cues can be recorded by having
microphones inside dummy head.
Or by putting small microphones
into ears of (hopefully) not so dummy head.
In games we can't do that kind of recording, so we have simulate binaural sound/behaviour of sound waves on their way to ears mathematically.
That's the job of Head Related Transfer Function algorithms.
Most sound cards have had those for decade, with Creative having some of the best HRTF algorithms.
(of course HRTFs use average head shape, so if your head shape is farther from average immersion suffers)
Once having binaural signal it's up to headphones.
With good headphones besides directionality there's also actual feel of distances, instead of sounds coming from next to ear.
First minute of this is excellent quick test for headphones, with sounds coming from difference directions and distances:
With bad inaccurate headphones immersion collapses to "head in bucket under water".
If you don't need closed design for isolation sounds of noisy environment, open headphones have easier time in necessary signal reproduction accuracy.
So closed headphone for noise isolation, or quiet environment and open headphones is first choise to do.
Then there's preference of do you want fun above neutral bass punch, or neutral bass and maximal details like foot steps etc?
Though in case of closed headphones bass tends to be very strong or very weak.
Open headphones are easier to balance in that.
For closed design Beyerdynamic DT770 would be good for its price, though closed designs bass could do with equalziing down if you want better details.
For open Headphones Beyerdynamic DT990 Pro does good balance of bass immersion and details.
AKG K702 again is aural "god mode/wallhack" for details with its accurate neutral sound.