What kind of music do you listen to? I find headphones differ a lot with music, some I tryed sound awesome with hard rock/dominant vocals sharp drums and punchy bass but dont sound good with hip hop rap ect... And others sound awesome with hip hop but lack the strong mids it takes to reproduce voice well...
Anyway, if your budget is $350 just for headphones I use AKG k267 and they are pretty much $350 exactly. They have an awesome sound, I love them for rock, country, classical, jazz, R&&B, rap, ect.. A good all around set...
Now if you dont care about bass much, and dont listen to much rap r&B ect.. Than look into HD25's, I have a set and they cost much less, Not crazy about how they reproduce low digital bass {rap hip hop ect} stuff like Black eyed peas with low lows isnt GREAT, but still very nice set also...
As far as what to plug them into, you will notice a world of difference going from your direct plugin methos to a Audioengine D1 DAC, best $150 you will ever spend.... I have one double sided taped to the monitor of my laptop {I own 3 all together}....
Good luck, I dont know much about other sets, since I have only owned 3 sets my entire life, but the 2 I listed should be a good start..
Also both a very comfortable.. I hope I am talking about the rite headphones with you, because the G930s are more of a "gaming" headphone, I know very little about them except my kids have g35's they use for gaming... Arent them wireless? The 2 I listed have no mics and are for music...