[KStreetSounds]

I recently re-discovered the world of higher quality sound and have been on a tear upgrading my equipment. Recently bought a Onkyo receiver from a friend who wasn't using it, and promptly upgraded the HTiB speakers to NHT Classic Three's. 
 
Now time to pick headphones... I've been reading threads for a few days but haven't been able to sort through the information-overload. Hoping someone can help me out.
 
My criteria:
 
(1) around-ear / closed-back.  I spend a lot of time on trains, in airports etc... and want some level of isolation and minimal leakage.
 
(2) $300 or less, new.
 
(3) Somewhat collapsible... don't want them to take up TOO much space in my bag when traveling (also somewhat durable/rugged).
 
(4) Excellent and versatile sound quality. I have very eclectic musical tastes, for example (in no order):
     - Dave Matthews Band
     - Bon Iver
     - Daft Punk
     - Classical Symphony
     - DJs (Girl Talk / Tiesto / Skrilex)
     - Classic Rock (Fleetwood Mac, Pink Floyd, Billy Joel)
     - Jazz (i.e. Miles Davis)
     - Iggy Azalea (just kidding)
 
(5) Primary source will be Fiio X5 playing FLAC files ripped from CDs (unless someone recommends a better DAP/DAC for the same price or lower).
 
Please let me know if anything else matters!
 
THANK YOU

 

[KStreetSounds]

Also, I currently use Bose AE2.  While overpriced, they are quite comfortable. Would love my next pair to be just as comfy.

 

[Lorspeaker]

i do like the bose AE2... hmmm, if u still want to move "up" , 
try the yamaha MT220, definitely a CLEAR UPGRADE..
but it isnt foldable, it is quite light though. v easy to power.

 

[Youth]

DT770 Pro 80 ohm
DT150

 

[KStreetSounds]

  DT770 Pro 80 ohm
DT150

 
DT150 looks ridiculous.
 
Would 80 ohm headphones strictly limit me to the Fiio X5, or would they also work for occasional iPhone or laptop use?  Similarly, would the 32 ohm version be OK with the X5?  Basically asking which is more flexible.
 
I've seen the 770's described as both "neutral" and "bass monsters".  Lots of conflicting opinions?
 
How would the 770's compare to Senn HD 25-1 II or the HD-380? 

 

[Youth]

   
DT150 looks ridiculous.
 
Would 80 ohm headphones strictly limit me to the Fiio X5, or would they also work for occasional iPhone or laptop use?  Similarly, would the 32 ohm version be OK with the X5?  Basically asking which is more flexible.
 
I've seen the 770's described as both "neutral" and "bass monsters".  Lots of conflicting opinions?
 
How would the 770's compare to Senn HD 25-1 II or the HD-380? 

 
80 ohm has more bass than the 32 ohm version but the 32 ohm can run straight from an iPhone, so it's more flexible. They are not "bass monsters" but they do have bass. 
 
Sorry I dont know those.