New Headphones + Amp Recommendations?

Hi,

I currently have a Cowon J3 with a complete FLAC library paired with Klipsch S4 headphones. I am wanting to move on and get a nice set of cans, hopefully to enhance my audio experience and am wanting recommendations. I would like to spend no more than $500 for a combined pair of headphones and an amp.

I've been looking at a few sets of cans, which include:

AKG K702
Beyerdynamic DT 880
Audio-Technica ATH-M50
Grado Prestige Series SR-60i

I have no experience with amps, but have been looking at:

HeadRoom Total BitHead
HeadRoom Total AirHead
iBasso T3
Rockhopper Mini3

I may not have made it obvious, but I'd like the setup to be portable enough where it's not a hassle for me to carry around.

My music selection varies from vocal -> classical -> jazz -> rock -> rap / hip-hop. So I guess a headphone that is great all around is desired.

Thanks!

Edit:  I guess I haven't even really considered open vs closed headphones.  I guess my listening environment isn't extremely loud for the most part (walking around campus), but I guess I'd like to use them on a plane or something when I take trips and such.

I'm starting to lean towards the HD650's which can be had for about $350.  I also found a used cardas audio cable for them for around $100. 

Any recommendations of a good amp to pair with these?

Would any of these amps work?

http://www.headfonia.com/music-on-a-budget-sub-100-portable-amps-shootout/

Or the Headroom Total Bithead / Airhead?