Heyy Lazostat, how are you doing..
First of all " high quality sound" = a very very huge thing.
Well, do you want audiophile grade suiltable audio?
Or, just many people even like bit bass added things also.Many like mids high with treble.Many like bit suppressed range!! ....etc etc etc...But in exact technical language things will be bit different sounding.
And quality also depends on the source with which you are using your headphones.So the source is among the most important things along with your headphones. How much or what's the way it drives your headphone that matters.Some like higher Sound pressure in headphones.I like personally!
Well so what I am trying to say if you say bit more like what you want or with which source you want to use them(not much ,but if possible little more

) then anyone here will be able to help you much better!
And lastly I will tell you one thing, best is that whatever pleasing your ear.That's it.Not technical Detalis and all etc...So why dont you try few headphones by yourself in showrooms. I mostly do like that!!!
If you want to use G6, and want in-budget headphones then why dont you try sennheiser CX 3.0? Or older model CX 300 II ! Its in-ear actually!!..I used both but with sony XB 70 AP earbuds.I found more suitable in my ear with those earbuds.They sound Good!!!
Enjoy audio