OP, I myself am looking to get a new pair of headphones to compliment my Pro 900 and so far have come to this setup after some research.
My music tastes vary slightly from your own (electro-house, EDM, etc) but I do also listen to J-rock and K-pop, which have the same types of musical elements you may find in anime OSTs.
I've found that my Pro 900 is very well suited to pure EDM but vocals sound a bit lacking, mids are recessed and guitars don't sound quite 'right'. You should probably rule this headphone off.
In my research for a 'companion' pair of headphones with the Pro900 I was quite tempted by the D2000 but after reading some reviews and comparison, I think the Sennheiser house sound of rich mids and lows are better suited to the sound profile I want for music other than EDM. To this, I decided on the HD650 which is 'bassier' than the more balanced HD600 (I still can't shake off my basshead tendencies).
I believe that unless you have preference over bass, the HD600 would be better suited to you. Just note that the D2000 is closed (won't leak sound excessively) and the HD6xx are open (ditto).
Now for the DAC and amplifier, I've asked around and some members here found that a HRT Music Streamer II ($150) and a Schiit Asgard ($250) have good synergy with the HD600/650. This may be slightly over budget so perhaps a Tubemagic or some FiiO gear would be a better solution for you.
What I recommend
HD600 ($300) + HRT MSII ($150) + Schiit Asgard ($250)
$100 over budget unfortunately. Suggest you look around a bit more for your DAC/amp if you like.
Wel if I'm already posting, might as well answer your question.
The anime is Boku wa Tomodachi ga Sukunai or just shortened to Haganai. Airing this season. ^_^
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It would be good if
Dubstep Girl could step in and give some advice, she has most of the well respected headphones in 'mid-fi' and a WA6 to boot (very jelly of her).