The good thing about this update is that you can take advantage of Dolby Atmos music with any pair of headphones/speakers so long as you have the setting turned to "Always On" instead of "Automatic."
As far as lossless/hi-res - generally speaking, the more you spend, the bigger difference you'll be able to hear (to an extent). That being said...
I have both of these and love them both for different reasons. I've spent more on pairs of headphones in the past and these two top them all:
Sennheiser HD599 - $200
Audio Technica ATH-M50x - $150
I don't have these but I've heard good things (some of which are farther on the cheaper side):
Philips SHP9500 - $60
AKG Pro Audio K72 - $40
Beyerdynamics DT 770 PRO - $150(ish)
Audio Technica ATH-M40x - $100
Other than that - you can google "best budget headphones" and there's a ton of lists. For audio stuff I'd stick to What Hi-Fi?, Crutchfield, Wired, and RTINGS as much as you can for the most reputable reviews. There are a bunch of Reddit threads discussing (read: arguing about) headphones, too. Happy listening!
Just noticing the 250 ohm version is only $170 on Amazon. Good deal for the 80 ohm version though.
I'm really sorry you missed out on the MassDrop 6XX's, but for the money I don't think you can go wrong with Audio-Technica MX-50, Sennheiser 595-C, or Beyerdynamic DT 770 PRO, 250 ohm. Of these I like the Sennheiser the least, but for a bit more money the Sennheiser 598s sound noticeably better if you don't mind open back which will bleed noise.