In my opinion, for affordable audio nirvana, you need three things to check. First, you need a set of reference speakers that are accepted & measured as such (probably from this site), and that will be your benchmark or neutral sound/tonality. Secondly, you need a set of headphones that provide for you the same neutral sound/tonality as your reference speakers - this is harder to achieve due to natural physical antatomical deviations between people and by extension you have to be lucky for instance if you EQ the headphone to the Headphone Harman Curve and it happens to be neutral for you (as it is for me mostly) then you can compare your headphone sound on your favourite and well known tracks to that on your speakers....thereby knowing that tonality wise they are the same or very similar. Once you know your headphones are tonality wise the same or very similar to your reference speakers then you have the advantage of enjoying room mode free clear bass on your headphones, but only if the third criteria is satisfied. The third criteria is that you've chosen some headphones that can play low bass without significant distortion and also chosen headphones that can go at least most of the way to satisfy the spatial qualities of a 2 channel speaker system, and by this I mean the "soundstage" quality, and in my experience my AKG K702 is the only headphone that does that for me, but for you that might not be the case. So there's a few hurdles to cross, and a lot of luck required to hope that you meet the Harman EQ criteria which enables you to easily EQ your headphone to neutral as well as build in some spatial qualities within that frequency response. Unfortunately, there's a lot of hurdles to cross, and you have to be lucky at a number of stages in terms of if the Harman Curve fits you combined with choosing a headphone that can satisfy the spatial needs whilst also being EQ'able to that Harman Curve. This is my experience re headphones after trying a number of different models and also whilst owning a reference speaker system & whilst confidently manipulating EQ on both my speakers & headpones, I feel I'm very lucky in how all the dice have landed, but this is my take on how to achieve cheap audio nirvana.....ultimately through headphones - because it's more expensive but less complicated through speakers! If headphones didn't work for me like they do, then I would be investing more in speakers, and that would cost a lot more in speakers & also in room treatments and room EQ efforts.
(That's not to say I don't enjoy listening to my speakers, it's a more social event and I can move around more and you feel the bass rather than just hear it, but to be honest the Harman Curve has increased bass to make up for that deficit, but it's not quite the same.....but at the same time the headphone bass is a lot clearer & better defined.....it's just a different experience......so speaker music is still important to me, just I probably would have put more effort & money into my speakers if my headphones didn't satisfy me as much).
Headphones is really luck of draw all things considered.....luck.