What do you care about in this hobby?

I can only respond from my perspective and I do not believe we can reach an axiom, for this is a subjective hobby.  I am first a lover of music, especially live, acoustic musical performances as well as recorded performances.  Therefore, composition and performance transcend the ability of any system to reproduce the recording of the subject piece.  Recordings of favorite compositions can bring a tear to my eye and affect my soul listening in my backyard with a plastic glass of gin, lemonade, and mint sprig in hand, on a Bose portable mini, as well as with a Riedel goblet of a 95+ rated Amorone on my main rig. However, I am an audiophile not only from the musical appreciation perspective but also from the perspective of the system’s ability to reproduce the emotional experience of the composition and performance and bring me closer to memories of the emotional experience of attending live acoustic musical performances.  Whether you like or hate his publications, I am a  disciple of  Harry Pearson and the lexicon and philosophy of evaluating systems in the established in 1970s.  The goal of approaching “The Absolute Sound” in reproduced music is unrealistic (a whole other discussion), but for me, it is a goal of providing a glimpse of the absolute sound, which from my perspective, amplifies the emotional experience I receive from the recorded piece.  I find the engineering of the recording the limiting factor more so than the system. So, after much pontificating to reach a conclusion, music does transcend any inabilities of a system (or recording) and it is not the arbitrary all-consuming accuracy of the system (or recording) itself that is more important to me.  However, the system (or recording) can enhance or diminish my emotional  experience to a piece, leading to my original statement that I have heard expensive systems that did not let me connect emotionally to familiar recordings as well as less expensive systems.  

"E's off his meds again....*sigh*  Bring out the net and the long-sleeved canvas coat...."  

A court order is just a sheet of paper, they can't keep me from my chosen state of minds.  

To me, this hobby is all about a form of minMax optimization, i.e., minimal cost and maximal performance.  Nothing less.  Nothing more.

@mapman  More on eliciting emotional response as what I care about in this hobby … what are the attributes of sound reproduction that elicit emotional response for me.  
 

While in a broad sense many will consider the ability to elicit emotional response a subset of the sound quality category you list, I consider emotional response a separate category.  The attributes I will describe cannot elicit emotion individually, but rather together reinforce each other creating a sum greater than the whole. The ability to meld these attributes in a cohesive manner to reinforce each other is achieved to a greater or lesser degree depending upon the system and how well the individual components integrate together to reinforce each other.  Ok, long winded again.  What are the attributes of a system that elicit emotional response to me?   I have listed them in what I consider the order of preference.  

1. Timbral accuracy, including the necessary resolution to develop the color and shading of instruments 
2. PRAT, including the resolution of micro and macro dynamics that bring life to the impact of the first wave but also to the secondary harmonics and ambient decay. 
3. Bloom, That elective midrange quality that makes reproduced music sound natural and liquid like I hear when sitting first tier in the Met, Koch, or Carnegie.  
4. Image density and dimensionality, that must be natural and not exaggerated.  
5. Wide frequency response with an accurate but sweet treble and extended bass, balanced throughout the range. 
    

When there is synergy between system components, these qualities reinforce each other to reproduce the emotion of the composition and performance.  Some systems may do some but not all well.  That is why I consider it a separate and critical category.  Systems that do all well in a cohesive manner, elicit more emotional response to the music for me. The sum is more important than the individual.  

Sound quality but value for money. Value can be technical acheivment, part selection, engineering. Also interesting cabinet materials and design. Is there a synergy?