Interesting to note responses.
If your listening preference is analytical, cerebral the criteria will be different than if your listening preference is for emotional impact. Nice to see that some of the responses include both.
In his well known book Get Better Sound, Jim Smith writes that emotional impact is created by three things, 1) Rhythm (accurate timing, that is, when all frequencies reach the ear at the same time - this is what gets my toes tapping and my head nodding), 2) Timbre ("tonality", the precise reproduction of harmonics, overtones, what makes an "A" on the piano,violin, saxophone, acoustic guitar, electric guitar, male & female voices sound different - this is what I find to be nurturing), 3) Dynamics (the variations in loud/soft, fast/slow, flowing, continuous/sharp, percussive, compare strings to the abrupt almost harsh shimmering attack of cymbals - these contrasts are what hold my attention and keep me engaged).
Decades ago I started my audiophile journey listening cerebrally, critically while noting what moved me as secondary. I was listening to my system. At some point about 6-7 years ago I found it difficult to listen to my system anymore . . . . because the music kept distracting me and after some time I'd notice my eyes were closed and my body was moving. I'd forgotten to listen for whether the new preamp improved the sound stage, or the texture of the instruments (timbre) or the retrieval of detail. Finally I gave up and learned to just float in the music. A side benefit has been that this addiction has been costing less money. I am now clearly one who listens for emotional nourishment rather than cerebral satisfaction though I didn't start here.
There is no "one size fits all", no "best". May you find what you personally enjoy most.