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

The room, setup, and placement are huge factors. Assuming the gear is good, and cables aren’t the weak link, speaker placement is typically low hanging fruit. I tend to use the music I listen to most as my reference, at least the ones that are decent recordings. Some recordings have more bass, some less, so it’s good to find a happy medium with the stuff you listen to most often.

Isolation of your gear is another subtle way to optimize things, and squeeze a bit more refinement....TT, amps/pre, speakers. TT and preamp are on sorbothane feet. speakers are on isolation spring pucks, amps are on rubber/cork feet.

I tend to use tube rolling and cable changes for final tweaks to dial in the sound I want. There are really no hard fast rules....it’s very subjective, and very unique to your setup, so you have to experiment a bit.

Once I was pretty happy with the overall balance, presentation, and synergy is about the time I started upgrading power supplies and opamps in my DAC and phono stage for a bit more refinement.  Wall warts got replaced with linear regulated power supplies.

Do it step by step, one at a time - that's an excellent advice.

Looking for best pressings is an almost never ending process, but before that you have to find out what the best pressings are. Sometimes it's difficult to know before actually comparing. But this can make very big differences.

My turntable is on a thick maple block which in turn is on the floor. There are big Boston Audio graphite tune blocks under the maple platform. Seems to work fine. Integrated tube amp is also on a thick maple block which is on the floor with Audiopoints brass cones under it. Two tape decks and PS Audio regenerator are on the rack. The Salamander rack is no good but since both the turntable and amp are on the floor, I see no reason to replace it.

Tubes in the amp are excellent, all NOS Mullards and RCAs. I do have to replace tubes for the phono, probably with Mullards or RCAs but might try Raytheon black plates.

Cables are more than adequate, and Nottingham Spacearm's cable goes from the cartridge right into the onboard phono stage amp, no need for separate tonearm cable or interconnects. The table has Boston Audio graphite mat instead of stock.

So, I am not sure what I might want to do in terms of fine tuning. Perhaps some feet under the amp.

Speakers are placed as well as they could be in the room, and most of the listening is close to near field listening.

Fine tuning for me is not necessarily linear path, always about determining the weakest link. Not being afraid to experiment and fail is required, weakest links may not always be obvious. In the end everything matters, sometimes the smallest changes can make all the difference, tuning is an art rather than science.

Tuning is an art indeed.

Leaving wall current alone - it’s a separate big problem. Leaving the room alone too.

Do you begin by seeking out best LP pressings ? Or tube rolling ? Or cables and power cords comparisons ? Isolation devices perhaps ? Something else ?

How do you go about it ?

I tend to start from the beginning - LP pressings.

I have never felt "wall current" or power issues to be a limiting factor, at least where I reside. Room issues are mitigated by my choice of speakers (Tannoy), "mid-field" setup, and light treatment of 1st reflections. Positioning is key.

I obsessed over tubes for a while and have a ton, but it’s not as big a deal to me now. Choosing the right power tube for the amp can be important.

For cables - speaker cables, specifically its silver content, has had the most effect. I like some good solid silver on this link. Large gauge. It definitely sounds different from copper. Unfortunately, it has become prohibitively expensive in modern cables. I buy used.

The biggest issues are: 1. choosing your transducers, and 2. matching your components and transducers to each other. Call this "synergy" or whatever. This is the biggest factor in getting a system to sound good, for me. At this point, I have collected several of every kind of component. The sonic differences by each component (and combination) are very noticeable, and "portable" even to different systems / rooms. 

For recordings - no I’m not going out of my way to seek special recordings. I have some, and they’re great, but are not available for most material. Perhaps 50 - 70% of my vinyl collection sounds "really good" to "great" as is. And I’m grateful for that. Digital has a lower % than this, but there are some bangers in there too.