Big-time headphone person here (@Pharmaboy on Head-Fi). I own a lot of stuff and often review loaner headphones, amps, DACs.
Everybody hears the same things quite differently, so I can only respond from my own experience and sonic tastes:
- DAC: Consider either an R2R (resister-based) DAC, or a non-oversampling (NOS) DAC. Either one can be had with a tube output, if that’s your thing (it’s definitely my thing). Either R2R or NOS digital will change how you perceive digital. Not only is it far less edgy and "processed" sounding then delta/sigma, chip-based designs, but the notes tend to have real weight and body. My best non-tube output NOS DAC is the Metrum Onyx. If you can find one of those, it’s endgame for as long as you want it to be. Many recommend this tiny Laiv NOS uDAC, said to sound great, but has only balanced outputs (2 x 3-pin XLR), which might be a barrier for some.
- Headphones: Difficult because prices vary wildly. I’m a huge fan of ZMF headphones, which veer towards the musical (and physically beautiful) design camp. If you can pick up a gently used Aeolus (open-back) or Bokeh (less expensive closed back), you’ll be quite surprised at how non-edgy & annoying headhphones can be. For a more budget-friendly new option, there’s always the HFA Dahlia 2 (I really liked the sound at CanJam):https://hififorall.com/products/hfa-dahlia-2-headphone
- Amps: Again, difficult because prices vary wildy, also because you have to decide whether you need balanced output (I do because all my headphone cables are 4-pin XLR). My favorite amps are by Violectric. I just reviewed the V222, a compact, wonderful-sounding balanced desktop amp. You can get one new for a little under $1,600 from a terrific dealer, Power Holdings Inc, or look for one used