Fine tuning the system. Where do you start and how do you proceed ?

I apologize but it is my opinion that there is no definitive starting point but rather process of optimization by experimentation.  I recommend your starting point is listening to acoustic and amplified music and developing your perception on how you believe reproduced music should sound.  Then you should choose recordings you feel are well engineered with clarity, timbral accuracy, dynamics, and bass and treble response.  The next step is to critically listen to your system and determine which SQ attributes you wish to optimize, for this will determine the actions you take to reach your goal.  For example, if you to solidify imaging and or tighten bass with no capital purchases, you would start with speaker placement and room treatment.  If you are hearing high frequency mains distortions like glare you will need to experiment with cords, conditioning or regeneration.  I could go out on a limb and give you a general order of importance- speakers, speaker placement, room treatment, front end (DAC/Steamer or TT/arm/cartridge/phono pre), amplification (pre/power/int), speaker cable, interconnects (including digital) power cords, power conditioning, vibration isolation.  However, listen and set a goal on what SQ attribute you wish to improve.  Use the process I recommend to do this.   Then research in the press solutions or ask specific questions on how to improve that attribute in this forum.  There are many more knowledgeable than I that I am sure will assist at that point. By using a process of establishing a specific goal and achieving that goal you have a greater chance of reaching a point is satisfaction, and not constantly chasing change for the sake of change.