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

I strongly agree that source material has a HUGE impact on how a system will sound, and the right "LP pressings" is the source material that offers the most potential for reaching the pinnacle of this hobby.

However, I'd say that using a record to make a system change is less about "fine tuning" and more about discovering that a great sounding copy of a great record and others like it (meaning other extremely high quality pressings of other titles) requires that we build a system that can bring the recordings on that record to life in the most convincing and satisfying way possible.

IOW, once you start playing truly great sounding records (I'm talking vetted, vintage records here, not the so called "audiophile" records that are released these days) you realize that you need to go back to square one and build a system that can actually play those records, because hardly any system can.

Therefore playing the right "LP pressings" is more about system design than it is "fine tuning". You want to start with those records, not finish with them!

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.  

@inna ...Now digest all of the personally pertinent parts of the above...

And go have fun following your muse... ;)

Tuning and fine tuning with tubes is a great way to improve the sound or simply to make it slightly different. It can be like putting different strings on the same acoustic guitar.

Playing with isolation/resonance control devices could be fun, but I don't have energy and funds to approach it seriously. This would require tremendous work to find the overall best solution.

When doing fine tuning it would be wrong to dissect the sound. This is the final polishing, the sound is already excellent.