Get a used Asus Xonar DX or D1 sound card ($?) and a EPH-02 (99 GBP) headphone amplifier.
The Xonar DX/D1 comes with a CS4398 DAC chip and an audio processor (for Dolby Headphone Surround Sound), just need to plug the EHP-02 into the Xonar and your headphones into the EPH-02.
Or something for a little bit better audio quality (and more cash), the Audio-GD NFB-15.32 DAC/Amp, costs about 190 Euros, plus 30 Euros for shipping.
I just placed an order for one three days ago.
Then spend the rest of your budget for headphones.
(Optional, maybe 50 Euros for a used Sound blaster Z sound card)
Now I need to concentrate on headphones.
What would the cheap Stax setup be?