Another option to consider, if you are prepared to use your PC as a transport would be:
PC + Apple Airport Express
to
DAC (Beresford or DacMagic £150 to £200)
to
Headphones Amp (say 2nd hand MF X-CAN v3 £150)
to
Headphones (say £100 Grados)
I would recommend buying amps 2nd hand from eBay and the v3 version of the MF is very good - I have one myself
The Beresford DAC can also act as a preamp (new model) and a headphone amp however I myself find the MF X-Can v3 superior as an amp to the amp in the Beresford DAC.
I firmly believe that such a setup would destroy a CD player based solution in a similar price range.