It's impossible to define an emotional response, because it is so subjective and cannot be correlated to the normal objective criteria associated with evaluating equipment. Newbee's plight- listening to the system, rather than the music, is a common one- and a trap i have fallen into myself. (My way out of that is to get the system to a level that surpasses my expections, through a combination of equipment selection, room treatment and tweaking and then just sit back and enjoy- sure I do 'reality checks' and sometimes get neurotic- am i hearing a spurious noise, is the VTA right, should i adjust the crossover, but, at least right now, my system is working to its highest level yet, and I can enjoy the music, and worry less about the set-up).
No system is going to reproduce all records with the same level of engagement- that goes back to the earlier comments about how a good system is revealing in the differences it demonstrates between recordings.
I've been around the 'high-end' (i use that term recognizing it is both loaded and meaningless) since the early 70's and have heard expensive systems that are not engaging and modest systems that are. How to predict what combination of components works? Leaving aside the subjective elements of what the listener prefers (more analytical, more romantic, emphasis on soundstaging/bandwidth/etc.), it all comes back to the recognition of a reproducing chain, including the room itself, as part of a system. (You can include within that the recording itself, but we have little control over that).
Get the basics right first, room, good AC power, and then its more in the nature of synergies among the equipment, including the cable. How to do it predictably? Pretty hard. We have a lot of anecdotal information, including on Audiogon, about what components seem to work well with each other.
Despite the ideal that a good amp or good speaker should play equally well with other components, I'm not sure that's true. And, invariably, certain basic choices in equipment are going to dictate the associated equipment and ultimate sound. For example, I'm using horns, not everybody's cup of tea, but apart from all the other 'hi-fi' attributes, i want a sense of 'aliveness' to the system. That in turn dictates the kind of amp that best suits the speaker (an SET tube amp) and so on. Someone else may not want to make the tradeoffs I do, and desire a different set of priorities in what they perceive as ideal.
Whatever the path, the system should engage you. Not on all records- that's too much to ask, given the wide range of quality of different recordings. What's interesting to me is that as I have gotten my system to its best level of performance yet, I can enjoy lesser recordings for their music, even though I can obviously hear the difference between the lesser recording and the 'better' one.