Superlux HD681 Evo (offbrand AKG) + cheap USB DAC (FiiO E10K or so) + Equalizer APO (https://github.com/jaakkopasanen/AutoEq/tree/master/results) = basically as good as it gets, without breaking the bank.
Could you recommend a different one? I'd like to go and test that since my headphones broke last week and I've been too lazy to dive into the audiophile depths.