Most detailed cans + player, budget ~800$

[keyb_gr]

I'd look into K601, DT880 and maybe HD600. Be aware that the AKGs are a little hard to drive (not quite as much as the 701s when going by the specs, but still not a terribly easy load) and thus may benefit from an amp. Sheer volume on the Clip+ should be high enough in any case, though you may get within 10 dB of maximum on classical with replaygain on.