Sub $500
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Audeze iSine 20 w/cipher cable and iPhone/iPad. If you can’t find it, then the cheaper sibling, iSine LX or iSine 10. Cipher cable has it’s own DAC.
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Dragonfly Black w/Jitterbug, Grado SR 60/80/125 with tape mod OR Sennheiser HD-58x
$1k-2k
Schiit Lyr3, Schiit Bifrost 2, Sennheiser HD-6xx
$2k-5k
Schiit Bifrost 2, STAX SRM-T1S (used, Mjolnir modified), Hive Nectar eStat headphones
No experience above that.
Reasoning. That mid price point is tricky. I went for best DAC and AMP and scalable headphone, but the Schiit stack can be used with much better headphones to good advantage.
I’m not recommending stuff I haven’t heard. The STAX amps show up from time to time on Birger’s site, and there are alternatives.